11. Pielikums

III.Noteikt, kuras no dotajām funkcijām ir pāra funkcijas, kuras - nepāra funkcijas.

V. Katrai no dotajām funkcijām atrast apvērsto funkciju un noteikt apvērstās funkcijas definīcijas un vērtību apgabalu.

VI.Lietojot virknes robežas definīciju, pierādīt, ka $\lim\limits_{n\rightarrow\infty}a_n=a$ . Skaitlim $\varepsilon=0,01$ atrast atbilstošo

$\displaystyle 1.$	$\displaystyle \;\;a_n=\frac{4+2n}{1-3n},\;\;a=-\frac{2}{3};$	$\displaystyle 2.$	$\displaystyle \;\;a_n=\frac{3n-2}{2n-1},\;\;a=\frac{3}{2};$
$\displaystyle 3.$	$\displaystyle \;\;a_n=\frac{7n-1}{n+1},\;\;a=7;$	$\displaystyle 4.$	$\displaystyle \;\;a_n=\frac{n}{2n+1},\;\;a=\frac{1}{2};$
$\displaystyle 5.$	$\displaystyle \;\;a_n=\frac{5^n-1}{5^n},\;\;a=1;$	$\displaystyle 6.$	$\displaystyle \;\;a_n=\frac{5n+3}{2n-1},\;\;a=\frac{5}{2};$
$\displaystyle 7.$	$\displaystyle \;\;a_n=\frac{n^2+4}{5n^2-2},\;\;a=\frac{1}{5};$	$\displaystyle 8.$	$\displaystyle \;\;a_n=\frac{3n^2+1}{n^2+4},\;\;a=3;$
$\displaystyle 9.$	$\displaystyle \;\;a_n=\frac{n-2}{n+2},\;\;a=1;$	$\displaystyle 10.$	$\displaystyle \;\;a_n=\frac{7n+4}{2n+1},\;\;a=\frac{7}{2};$
$\displaystyle 11.$	$\displaystyle \;\;a_n=\frac{3n^2+1}{5-n^2},\;\;a=-3;$	$\displaystyle 12.$	$\displaystyle \;\;a_n=\frac{5n-2}{7n+3},\;\;a=\frac{5}{7};$
$\displaystyle 13.$	$\displaystyle \;\;a_n=\frac{5n}{n+1},\;\;a=5;$	$\displaystyle 14.$	$\displaystyle \;\;a_n=\frac{4n+3}{8n-1},\;\;a=\frac{1}{2};$
$\displaystyle 15.$	$\displaystyle \;\;a_n=\frac{n+2}{n+1};\;\;a=1;$	$\displaystyle 16.$	$\displaystyle \;\;a_n=\frac{3-n^2}{1+2n^2},\;\;a=-\frac{1}{2};$
$\displaystyle 17.$	$\displaystyle \;\;a_n=\frac{5n^2-3}{3n^2+1},\;\;a=\frac{5}{3};$	$\displaystyle 18.$	$\displaystyle \;\;a_n=\frac{1-2n^2}{2-4n^2},\;\;a=\frac{1}{2};$
$\displaystyle 19.$	$\displaystyle \;\;a_n=\frac{4^n}{2-4^n},\;\;a=-1;$	$\displaystyle 20.$	$\displaystyle \;\;a_n=\frac{5-3n}{7n+4},\;\;a=-\frac{3}{7};$
$\displaystyle 21.$	$\displaystyle \;\;a_n=\frac{4-7n}{5-n},\;\;a=7;$	$\displaystyle 22.$	$\displaystyle \;\;a_n=\frac{5n-8}{3n+11},\;\;a=\frac{5}{3};$
$\displaystyle 23.$	$\displaystyle \;\;a_n=\frac{2^n-1}{2^n},\;\;a=1;$	$\displaystyle 24.$	$\displaystyle \;\;a_n=\frac{2n-3}{4n+5},\;\;a=\frac{1}{2};$
$\displaystyle 25.$	$\displaystyle \;\;a_n=\frac{5n+6}{n+1},\;\;a=5.$

VII.Lietojot funkcijas robežas definīciju, pierādīt, ka $\lim\limits_{x\rightarrow a}f(x)=A$ . Skaitlim $\varepsilon=0,01$ atrast atbilstošo $\delta$ .

$\displaystyle 1.$	$\displaystyle \;\;f(x)=3x^2-2,$	$\displaystyle \;\;a=-2,$	$\displaystyle \;\;A=10;$
$\displaystyle 2.$	$\displaystyle \;\;f(x)=3-\frac{x}{5},$	$\displaystyle \;\;a=-5,$	$\displaystyle \;\;A=4;$
$\displaystyle 3.$	$\displaystyle \;\;f(x)=x^2-x+2,$	$\displaystyle \;\;a=1,$	$\displaystyle \;\;A=2;$
$\displaystyle 4.$	$\displaystyle \;\;f(x)=x^2+2x+3,$	$\displaystyle \;\;a=0,$	$\displaystyle \;\;A=3;$
$\displaystyle 5.$	$\displaystyle \;\;f(x)=x^2+x+1,$	$\displaystyle \;\;a=3,$	$\displaystyle \;\;A=13;$
$\displaystyle 6.$	$\displaystyle \;\;f(x)=3x-2,$	$\displaystyle \;\;a=-3,$	$\displaystyle \;\;A=-11;$
$\displaystyle 7.$	$\displaystyle \;\;f(x)=3x+2,$	$\displaystyle \;\;a=2,$	$\displaystyle \;\;A=8;$
$\displaystyle 8.$	$\displaystyle \;\;f(x)=5-2x,$	$\displaystyle \;\;a=0,$	$\displaystyle \;\;A=5;$
$\displaystyle 9.$	$\displaystyle \;\;f(x)=x^2+x-5,$	$\displaystyle \;\;a=3,$	$\displaystyle \;\;A=7;$
$\displaystyle 10.$	$\displaystyle \;\;f(x)=3x^2-1,$	$\displaystyle \;\;a=2,$	$\displaystyle \;\;A=11;$
$\displaystyle 11.$	$\displaystyle \;\;f(x)=3-5x^2,$	$\displaystyle \;\;a=2,$	$\displaystyle \;\;A=-17;$
$\displaystyle 12.$	$\displaystyle \;\;f(x)=x^2+4,$	$\displaystyle \;\;a=1,$	$\displaystyle \;\;A=5;$
$\displaystyle 13.$	$\displaystyle \;\;f(x)=3x-2,$	$\displaystyle \;\;a=-1,$	$\displaystyle \;\;A=-5;$
$\displaystyle 14.$	$\displaystyle \;\;f(x)=x^2-3x,$	$\displaystyle \;\;a=3,$	$\displaystyle \;\;A=0;$
$\displaystyle 15.$	$\displaystyle \;\;f(x)=2x^2+1,$	$\displaystyle \;\;a=-1,$	$\displaystyle \;\;A=3;$
$\displaystyle 16.$	$\displaystyle \;\;f(x)=x^2-7x+1,$	$\displaystyle \;\;a=7,$	$\displaystyle \;\;A=1;$
$\displaystyle 17.$	$\displaystyle \;\;f(x)=x^2-6x+3,$	$\displaystyle \;\;a=6,$	$\displaystyle \;\;A=3;$
$\displaystyle 18.$	$\displaystyle \;\;f(x)=3x-5,$	$\displaystyle \;\;a=2,$	$\displaystyle \;\;A=1;$
$\displaystyle 19.$	$\displaystyle \;\;f(x)=x^2-8x+2,$	$\displaystyle \;\;a=-1,$	$\displaystyle \;\;A=11;$
$\displaystyle 20.$	$\displaystyle \;\;f(x)=x^2+4x+2,$	$\displaystyle \;\;a=-2,$	$\displaystyle \;\;A=-12;$
$\displaystyle 21.$	$\displaystyle \;\;f(x)=2x^2+1,$	$\displaystyle \;\;a=-2,$	$\displaystyle \;\;A=9;$
$\displaystyle 22.$	$\displaystyle \;\;f(x)=4x+7,$	$\displaystyle \;\;a=-3,$	$\displaystyle \;\;A=-5;$
$\displaystyle 23.$	$\displaystyle \;\;f(x)=8-5x,$	$\displaystyle \;\;a=0,$	$\displaystyle \;\;A=8;$
$\displaystyle 24.$	$\displaystyle \;\;f(x)=x^2+2x-3,$	$\displaystyle \;\;a=-1,$	$\displaystyle \;\;A=-4;$
$\displaystyle 25.$	$\displaystyle \;\;f(x)=x^2-2x-6,$	$\displaystyle \;\;a=-2,$	$\displaystyle \;\;A=2.$

$\displaystyle 1.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 2}\frac{x^2-5x+6}{x^3-8x+8};$	$\displaystyle 2.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -3}\frac{x^2+2x-3}{3x^2+14x+15};$
$\displaystyle 3.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 1}\frac{x^2-2x+1}{x^3-x};$	$\displaystyle 4.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 1}\frac{x^3+x-2}{x^3-x^2-x+1};$
$\displaystyle 5.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{1}{2}}\frac{8x^3-1}{6x^2-5x+1};$	$\displaystyle 6.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -2}\frac{x^3+3x^2+2x}{x^2-x-6};$
$\displaystyle 7.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 3}\frac{x^2-5x+6}{x^2-8x+15};$	$\displaystyle 8.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 1}\frac{x^3-3x+2}{x^4-4x+3};$
$\displaystyle 9.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 1}\frac{x^4-3x+2}{x^5-4x+3};$	$\displaystyle 10.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 2}\frac{x^3-2x^2-4x+8}{x^4-8x^2+16};$
$\displaystyle 11.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -1}\frac{x^3-2x-1}{x^5-2x-1};$	$\displaystyle 12.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{3}{2}}\frac{2x^2-x-3}{2x^2-5x+3};$
$\displaystyle 13.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{1}{3}}\frac{3x^2+5x-2}{1-2x-3x^2};$	$\displaystyle 14.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -1}\frac{x^2-4x-5}{x^2-2x-3};$
$\displaystyle 15.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -2}\frac{2-3x-2x^2}{x^2+x-2};$	$\displaystyle 16.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 3}\frac{3x^2-11x+6}{2x^2-5x-3};$
$\displaystyle 17.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 2}\frac{x^3-3x-2}{x^3-8};$	$\displaystyle 18.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{4x^2-3x}{2x^2-9x};$
$\displaystyle 19.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 2}\frac{x^2-5x+6}{x^3-2x^2-x+2};$	$\displaystyle 20.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{x-3x^2}{5x^3-6x^2+x};$
$\displaystyle 21.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{1}{3}}\frac{3x^2+2x-1}{27x^3-1};$	$\displaystyle 22.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 5}\frac{2x^2-11x+5}{3x^2-14x-5};$
$\displaystyle 23.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -2}\frac{x^3+5x^2+8x+4}{x^3+3x^2-4};$	$\displaystyle 24.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -1}\frac{x^3+4x^2+5x+2}{x^3-3x-2};$
$\displaystyle 25.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 1}\frac{x^3-3x+2}{x^3-x^2-x+1}.$

$\displaystyle 1.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{x-3x^2}{4-\sqrt{x+16}};$	$\displaystyle 2.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 1}\frac{3x-2-\sqrt{4x^2-x-2}}{x^2-3x+2};$
$\displaystyle 3.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 1}\frac{\sqrt[3]{x-2}-\sqrt[3]{1-x+x^2}}{x^2-1};$	$\displaystyle 4.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 2}\frac{x-\sqrt{x+2}}{\sqrt{4x+1}-3};$
$\displaystyle 5.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\sqrt{x+1}-\sqrt{x^2+x+1}}{x^2};$	$\displaystyle 6.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\sqrt[3]{1+x^2}-1}{x^2};$
$\displaystyle 7.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\sqrt{x^2+1}-1}{\sqrt{x^2+16}-4};$	$\displaystyle 8.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 5}\frac{\sqrt{x-1}-2}{x^2-25};$
$\displaystyle 9.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\sqrt[3]{1+x}-\sqrt[3]{1-x}}{x};$	$\displaystyle 10.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 4}\frac{\sqrt{1+2x}-3}{\sqrt{x}-2};$
$\displaystyle 11.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -8}\frac{\sqrt{1-x}-3}{2+\sqrt[3]{x}};$	$\displaystyle 12.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 3}\frac{\sqrt{x+13}-2\sqrt{x+1}}{x^2-9};$
$\displaystyle 13.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 16}\frac{\sqrt[4]{x}-2}{\sqrt{x}-4};$	$\displaystyle 14.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -2}\frac{\sqrt[3]{x-6}+2}{x^3+8};$
$\displaystyle 15.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 8}\frac{\sqrt{9+2x}-5}{\sqrt[3]{x}-2};$	$\displaystyle 16.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\sqrt{1-2x-x^2}-1-x}{x};$
$\displaystyle 17.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\sqrt[3]{8+3x-x^2}-2}{x+x^2};$	$\displaystyle 18.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\sqrt[3]{27+x}-\sqrt[3]{27-x}}{x+2\sqrt[3]{x^4}};$
$\displaystyle 19.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 3}\frac{\sqrt{2x+3}-3}{9-x^2};$	$\displaystyle 20.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 1}\frac{\sqrt{x}-\sqrt{2-x}}{1-x^2};$
$\displaystyle 21.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{x}{\sqrt{x+4}-2};$	$\displaystyle 22.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -9}\frac{4-\sqrt{7-x}}{\sqrt{10+x}-1};$
$\displaystyle 23.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 1}\frac{\sqrt[3]{x}-1}{2-\sqrt{x+3}};$	$\displaystyle 24.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -1}\frac{\sqrt{3x+7}-2}{1+\sqrt[3]{x}};$
$\displaystyle 25.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 4}\frac{x-\sqrt{3x+4}}{16-x^2}.$

$\displaystyle 1.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{3x^3-9x^2+13x+1}{4x^3+8x^2-7x+16};$	$\displaystyle 2.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{4x^3+8x+7}{9x^3+11x+3};$
$\displaystyle 3.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{13x^2-2x+5}{x^4+6x+1};$	$\displaystyle 4.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{x^5-12x^3+7}{4x^4+8x^3+11};$
$\displaystyle 5.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{x^2-2x+5}{x^3+3x+7};$	$\displaystyle 6.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{2x^2+7x-1}{3x^2-5x+6};$
$\displaystyle 7.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{6x^2-7x-12}{2x^2-5x-8};$	$\displaystyle 8.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{x^2-4x+3}{x+5};$
$\displaystyle 9.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{x^4-2x^3-1}{100x^3+2x^2};$	$\displaystyle 10.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{3x^3-4x^2+8}{-5x^3+2x^2+x};$
$\displaystyle 11.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{5+3x^3}{7x^4-2x^2+1};$	$\displaystyle 12.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{2-x-4x^2}{x^3-7x+8};$
$\displaystyle 13.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{3x^2-2x-1}{7x-9};$	$\displaystyle 14.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{x^5-3x^4+7x-1}{3x^5+2x^3-3};$
$\displaystyle 15.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{3x^2-2x+10}{5x^3+3x-1};$	$\displaystyle 16.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{2x^3-3x^2+5}{3x^4-7x+1};$
$\displaystyle 17.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{3x^2-1}{5x^2+2x};$	$\displaystyle 18.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{6x^2+5x-1}{3x^2-x+1};$
$\displaystyle 19.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{1-x-x^2}{x^3+3};$	$\displaystyle 20.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{x^4-2x^2+3}{3x^3-5};$
$\displaystyle 21.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{x^2-1}{2x^2-x-1};$	$\displaystyle 22.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{2x^2+x-1}{x^2-5x+6};$
$\displaystyle 23.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{x^2-9x+14}{x^3+3x+14};$	$\displaystyle 24.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{10x^2+3x+1}{x^3-x^2-x};$
$\displaystyle 25.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\frac{x^2-5x-36}{2x^2-10x+12}.$

$\displaystyle 1.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{1-\cos^3x}{x\sin 2x};$	$\displaystyle 2.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{1+\sin x-\cos x}{1-\sin x-\cos x};$
$\displaystyle 3.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\left(\frac{1}{\sin x}-\frac{1}{\tg x}\right);$	$\displaystyle 4.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{\pi}{2}}\frac{\cos x}{\sqrt[3]{(1-\sin x)^2}};$
$\displaystyle 5.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{\pi}{6}}\frac{\sin\left(x-\frac{\pi}{6}\right)}{\frac{\sqrt{3}}{2}-\cos x};$	$\displaystyle 6.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{\pi}{4}}\frac{\cos x-\sin x}{\cos 2x};$
$\displaystyle 7.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{\pi}{4}}\frac{\sin x-\cos x}{1-\tg x};$	$\displaystyle 8.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{1-\sqrt{\cos x}}{x^2};$
$\displaystyle 9.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{x-\sin 2x}{x+\sin 3x};$	$\displaystyle 10.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\tg-\sin x}{\sin 3x};$
$\displaystyle 11.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\sin 5x-\sin 3x}{\sin x};$	$\displaystyle 12.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\cos x-\cos3x}{x^2};$
$\displaystyle 13.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{x\sin 3x}{1-\cos 3x};$	$\displaystyle 14.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{\pi}{3}}\frac{\sin\left(x-\frac{\pi}{3}\right)}{1-2\cos x};$
$\displaystyle 15.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{1-\cos 4x}{\sin^27x};$	$\displaystyle 16.$	$\displaystyle \;\;\lim\limits_{x\rightarrow-\frac{\pi}{4}}\frac{1+\sin2x}{\sin x+\cos x};$
$\displaystyle 17.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\sin x-\tg x}{4\sin^2\frac{x}{2}};$	$\displaystyle 18.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{\pi}{2}}\frac{\cos x}{\cos\frac{x}{2}-\sin\frac{x}{2}};$
$\displaystyle 19.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{\pi}{4}}\frac{1-\tg x}{\sin x-\cos x};$	$\displaystyle 20.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{1-\cos 3x}{\tg^26x};$
$\displaystyle 21.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\tg x-\sin x}{x^3};$	$\displaystyle 22.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\tg x}{\sin 5x-\sin x};$
$\displaystyle 23.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{1-\cos 5x}{x\tg 2x};$	$\displaystyle 24.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\cos 2x-1}{x\sin x};$
$\displaystyle 25.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{3x^2-5x}{\sin^23x}.$

$\displaystyle 1.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{\pi}{2}}(\sin x)^{\tg x};$	$\displaystyle 2.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{\pi}{4}}(\tg x)^{\tg 2x};$
$\displaystyle 3.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\left(\frac{x+1}{x-2}\right)^{2x-1};$	$\displaystyle 4.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\left(\frac{x^2+1}{x^2-2}\right)^{x^2};$
$\displaystyle 5.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{\pi}{4}}(\ctg x)^{\ctg 8x};$	$\displaystyle 6.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{\pi}{2}}(\cos 4x)^{\tg x};$
$\displaystyle 7.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{\pi}{2}}(\sin x)^{\ctg 4x};$	$\displaystyle 8.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\left(\frac{3x-4}{3x+2}\right)^{\frac{x+1}{3}};$
$\displaystyle 9.$	$\displaystyle \;\;\lim\limits_{x\rightarrow2\pi}(\cos x)^{\ctg x};$	$\displaystyle 10.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\left(\frac{x+3}{x-4}\right)^{\frac{x}{2}-3};$
$\displaystyle 11.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\left(\frac{x-7}{x-4}\right)^{\frac{x}{4}+5};$	$\displaystyle 12.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\left(\frac{x+5}{x+2}\right)^{\frac{x-1}{3}};$
$\displaystyle 13.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\left(\frac{2x-1}{2x+1}\right)^{x+3};$	$\displaystyle 14.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\left(\frac{x-5}{x-2}\right)^{\frac{x}{3}-4};$
$\displaystyle 15.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\left(\frac{5x-6}{5x-3}\right)^{\frac{x+1}{5}};$	$\displaystyle 16.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\left(\frac{3x-1}{3x+1}\right)^{x+4};$
$\displaystyle 17.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\left(\frac{x^2-1}{x^2}\right)^x;$	$\displaystyle 18.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\left(1-x^2\right)^{\frac{1}{\tg 2x}};$
$\displaystyle 19.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\left(1-\frac{1}{x^3}\right)^{x^2};$	$\displaystyle 20.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\left(1-\sin^2x\right)^{\frac{1}{x^2}};$
$\displaystyle 21.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\left(1+x^3\right)^{\frac{1}{\sin x}};$	$\displaystyle 22.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\left(1-2x^2\right)^{\frac{1}{\sin^2x}};$
$\displaystyle 23.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}(1+2x)^{\frac{1}{2\sin x}};$	$\displaystyle 24.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\left(1+x+x^3\right)^{\frac{1}{\sin x}};$
$\displaystyle 25.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\left(\frac{x^2-2}{x^2+3}\right)^{x^2}.$

$\displaystyle 1.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{2^x-1}{\ln(1+2x)};$	$\displaystyle 2.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\ln(1+\sin x)}{\sin 4x};$
$\displaystyle 3.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{1-\cos 10x}{e^{x^2}-1};$	$\displaystyle 4.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{1-\cos x}{\left(e^{3x}-1\right)^2};$
$\displaystyle 5.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\ln(1+10x)}{\tg x};$	$\displaystyle 6.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\ln(1-5x)}{\sin x};$
$\displaystyle 7.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{2^x-1}{\ln(x+1)};$	$\displaystyle 8.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\ln(1+\sin 2x)}{\sin 9x};$
$\displaystyle 9.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\ln(1+\sin 5x)}{1-\cos 10x};$	$\displaystyle 10.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{1-\cos 8x}{3^x-1};$
$\displaystyle 11.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{5^{3x}-1}{e^x-1};$	$\displaystyle 12.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{(e^{-8x}-1)x}{1-\cos 4x};$
$\displaystyle 13.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{3^x-1}{2^x-1};$	$\displaystyle 14.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\ln(1+3x)}{\sin 5x};$
$\displaystyle 15.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{4^x-1}{\sin x};$	$\displaystyle 16.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{e^{3x}-1}{\sin x};$
$\displaystyle 17.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\sin 2x}{\ln(1+x)};$	$\displaystyle 18.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{\ln(1+2x)}{\arcsin x};$
$\displaystyle 19.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{1-\cos 3x}{2\ln(1+9x^2)};$	$\displaystyle 20.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{1-\cos 6x}{\ln(1+3x^2)};$
$\displaystyle 21.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{5^{x^2}-1}{4^{x^2}-1};$	$\displaystyle 22.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{5\sin 3x}{e^{-3x}-1};$
$\displaystyle 23.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{x\sin 7x}{e^{-3x^2}-1};$	$\displaystyle 24.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{x\ln(1+4x)}{2\ln(1+2x^2)};$
$\displaystyle 25.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\frac{xe^{\frac{x}{2}}-x}{\ln(1+2x^2)}.$

$\displaystyle 1.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 0}\left(\frac{x^3-3x+1}{x-4}+1\right);$	$\displaystyle 2.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^{\frac{x+1}{x}};$
$\displaystyle 3.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 2}\frac{\log_3(7-x^2)}{2-x-x^2};$	$\displaystyle 4.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 5}\left(x-\sqrt{x^2-5x}\right);$
$\displaystyle 5.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 5}\left(1+\frac{4}{x}\right)^{\frac{x}{5}};$	$\displaystyle 6.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 3}\frac{\log_{19}(1+2x^2)}{4^x-62};$
$\displaystyle 7.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -1}\frac{\log_5(2-3x)}{x^4};$	$\displaystyle 8.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 2}\frac{x^2-x+1}{x-2};$
$\displaystyle 9.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 3}\frac{x^2-3}{x^2+4x-9};$	$\displaystyle 10.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 2}\left(\frac{3}{x^3+1}-\frac{1}{x+1}\right);$
$\displaystyle 11.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 22}\frac{x-6}{\sqrt{x+3}-3};$	$\displaystyle 12.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 2}\left(5+\frac{2}{x}-\frac{3}{x^2}\right);$
$\displaystyle 13.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 4}\left(x-\sqrt{x^2-4x}\right);$	$\displaystyle 14.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 6}\left(1+\frac{3}{x}\right)^{\frac{x}{2}};$
$\displaystyle 15.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -2}\frac{1+\sqrt{2x^2+1}}{x};$	$\displaystyle 16.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -3}\frac{6x^2+5x-1}{3x^2-x+8};$
$\displaystyle 17.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 3}\frac{9-x^2}{x^3-5x+2};$	$\displaystyle 18.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 2}\frac{x^3-4x+5}{x^2+6};$
$\displaystyle 19.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 1}\left(\sqrt{5x-4}+\log_2x\right);$	$\displaystyle 20.$	$\displaystyle \;\;\lim\limits_{x\rightarrow\frac{1}{5}}\left(x^3-\log_{\frac{1}{5}}x\right);$
$\displaystyle 21.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 4}\left(\frac{x-3}{x+1}\right)^{x-1};$	$\displaystyle 22.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 4}\left(x^2\sqrt{x+5}-x\sqrt{x}\right);$
$\displaystyle 23.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 6}\frac{\sqrt[3]{4x+3}-x\sqrt{x-2}}{2x-3};$	$\displaystyle 24.$	$\displaystyle \;\;\lim\limits_{x\rightarrow 2}\frac{\log_5(1+2x)}{x^2};$
$\displaystyle 25.$	$\displaystyle \;\;\lim\limits_{x\rightarrow -2}\frac{\log_{13}(1+3x^2)}{5^{-x}-1}.$

$\displaystyle 1.$	$\displaystyle \;\;\alpha(x)=1-\sin x,$	$\displaystyle \;\;\beta(x)=\cos x,$	kad $\displaystyle \;\;x\rightarrow\frac{\pi}{2};$
$\displaystyle 2.$	$\displaystyle \;\;\alpha(x)=\frac{x}{x-1},$	$\displaystyle \;\;\beta(x)=x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 3.$	$\displaystyle \;\;\alpha(x)=\tg x+x^2,$	$\displaystyle \;\;\beta(x)=x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 4.$	$\displaystyle \;\;\alpha(x)=2\sqrt{\sin x},$	$\displaystyle \;\;\beta(x)=x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 5.$	$\displaystyle \;\;\alpha(x)=1-\cos x,$	$\displaystyle \;\;\beta(x)=\sin x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 6.$	$\displaystyle \;\;\alpha(x)=x\sin^2x,$	$\displaystyle \;\;\beta(x)=x\sin x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 7.$	$\displaystyle \;\;\alpha(x)=\sin 2x-2\sin x,$	$\displaystyle \;\;\beta(x)=x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 8.$	$\displaystyle \;\;\alpha(x)=\frac{2x^4}{1+x},$	$\displaystyle \;\;\beta(x)=x^2,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 9.$	$\displaystyle \;\;\alpha(x)=5x^3+2x^2,$	$\displaystyle \;\;\beta(x)=3x^2+2x^3,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 10.$	$\displaystyle \;\;\alpha(x)=1-\left(\cos\sqrt{x}\right)^3,$	$\displaystyle \;\;\beta(x)=1-\cos x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 11.$	$\displaystyle \;\;\alpha(x)=\sqrt[3]{x},$	$\displaystyle \;\;\beta(x)=x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 12.$	$\displaystyle \;\;\alpha(x)=1-x,$	$\displaystyle \;\;\beta(x)=\sqrt{1-x},$	kad $\displaystyle \;\;x\rightarrow 1;$
$\displaystyle 13.$	$\displaystyle \;\;\alpha(x)=\sin 2x+x^2,$	$\displaystyle \;\;\beta(x)=x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 14.$	$\displaystyle \;\;\alpha(x)=2-2\cos x,$	$\displaystyle \;\;\beta(x)=x^2,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 15.$	$\displaystyle \;\;\alpha(x)=\cos 2x,$	$\displaystyle \;\;\beta(x)=\sin 4x,$	kad $\displaystyle \;\;x\rightarrow \frac{\pi}{4};$
$\displaystyle 16.$	$\displaystyle \;\;\alpha(x)=\frac{1-x}{1+x},$	$\displaystyle \;\;\beta(x)=1-\sqrt{x},$	kad $\displaystyle \;\;x\rightarrow 1;$
$\displaystyle 17.$	$\displaystyle \;\;\alpha(x)=1-x,$	$\displaystyle \;\;\beta(x)=1-\sqrt[3]{x},$	kad $\displaystyle \;\;x\rightarrow 1;$
$\displaystyle 18.$	$\displaystyle \;\;\alpha(x)=\sqrt[3]{x^2}-\sqrt{x},$	$\displaystyle \;\;\beta(x)=x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 19.$	$\displaystyle \;\;\alpha(x)=\sin 2x-\sin x,$	$\displaystyle \;\;\beta(x)=x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 20.$	$\displaystyle \;\;\alpha(x)=\frac{x(x+1)}{1-\sqrt{x}},$	$\displaystyle \;\;\beta(x)=x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 21.$	$\displaystyle \;\;\alpha(x)=\cos x-\sqrt[3]{\cos x},$	$\displaystyle \;\;\beta(x)=x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 22.$	$\displaystyle \;\;\alpha(x)=\frac{2x}{1+x},$	$\displaystyle \;\;\beta(x)=x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 23.$	$\displaystyle \;\;\alpha(x)=\sqrt{x+\sqrt{x}},$	$\displaystyle \;\;\beta(x)=x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 24.$	$\displaystyle \;\;\alpha(x)=e^{\sqrt{x}}-1,$	$\displaystyle \;\;\beta(x)=x,$	kad $\displaystyle \;\;x\rightarrow 0;$
$\displaystyle 25.$	$\displaystyle \;\;\alpha(x)=\sqrt{1+x}-1,$	$\displaystyle \;\;\beta(x)=x,$	kad $\displaystyle \;\;x\rightarrow 0.$

$\displaystyle 1.$	$\displaystyle \;\;f(x)=4x^2+6,$	$\displaystyle \;\;x_0=7;$
$\displaystyle 2.$	$\displaystyle \;\;f(x)=5x^2+x+9,$	$\displaystyle \;\;x_0=1;$
$\displaystyle 3.$	$\displaystyle \;\;f(x)=42x+3x^2,$	$\displaystyle \;\;x_0=2;$
$\displaystyle 4.$	$\displaystyle \;\;f(x)=x^3-x^2-4x+4,$	$\displaystyle \;\;x_0=3;$
$\displaystyle 5.$	$\displaystyle \;\;f(x)=2x^2+2x-3,$	$\displaystyle \;\;x_0=-1;$
$\displaystyle 6.$	$\displaystyle \;\;f(x)=2x^3+3x^2+5,$	$\displaystyle \;\;x_0=3;$
$\displaystyle 7.$	$\displaystyle \;\;f(x)=x^3+4,$	$\displaystyle \;\;x_0=1;$
$\displaystyle 8.$	$\displaystyle \;\;f(x)=x^2-5x+4,$	$\displaystyle \;\;x_0=2;$
$\displaystyle 9.$	$\displaystyle \;\;f(x)=x^2-3x-4,$	$\displaystyle \;\;x_0=2;$
$\displaystyle 10.$	$\displaystyle \;\;f(x)=x^2-x-6,$	$\displaystyle \;\;x_0=4;$
$\displaystyle 11.$	$\displaystyle \;\;f(x)=x^3-3x^2-x-2,$	$\displaystyle \;\;x_0=-3;$
$\displaystyle 12.$	$\displaystyle \;\;f(x)=x^3+x^2+4x-4,$	$\displaystyle \;\;x_0=1;$
$\displaystyle 13.$	$\displaystyle \;\;f(x)=x^3-9x^2,$	$\displaystyle \;\;x_0=-2;$
$\displaystyle 14.$	$\displaystyle \;\;f(x)=x^3+4,$	$\displaystyle \;\;x_0=1;$
$\displaystyle 15.$	$\displaystyle \;\;f(x)=3x^2+4x-4,$	$\displaystyle \;\;x_0=\frac{1}{2};$
$\displaystyle 16.$	$\displaystyle \;\;f(x)=2x^3+3x^2-7x-1,$	$\displaystyle \;\;x_0=0;$
$\displaystyle 17.$	$\displaystyle \;\;f(x)=x^3-5x^2+1,$	$\displaystyle \;\;x_0=2;$
$\displaystyle 18.$	$\displaystyle \;\;f(x)=2x^2-17x+35,$	$\displaystyle \;\;x_0=1;$
$\displaystyle 19.$	$\displaystyle \;\;f(x)=2x^2-7x-15,$	$\displaystyle \;\;x_0=\frac{1}{7};$
$\displaystyle 20.$	$\displaystyle \;\;f(x)=5x^3+2x^2+9,$	$\displaystyle \;\;x_0=-4;$
$\displaystyle 21.$	$\displaystyle \;\;f(x)=7x^2+3,$	$\displaystyle \;\;x_0=\frac{1}{3};$
$\displaystyle 22.$	$\displaystyle \;\;f(x)=2x^2-\frac{1}{3}x-\frac{2}{3},$	$\displaystyle \;\;x_0=3;$
$\displaystyle 23.$	$\displaystyle \;\;f(x)=x^2-x-4,$	$\displaystyle \;\;x_0=-5;$
$\displaystyle 24.$	$\displaystyle \;\;f(x)=x^2-8x+15,$	$\displaystyle \;\;x_0=4;$
$\displaystyle 25.$	$\displaystyle \;\;f(x)=9x^3+1,$	$\displaystyle \;\;x_0=-3.$

XI.Atrast funkcijas pārtraukuma punktus un noteikt to veidu. Konstruēt funkcijas shematisku grafiku.

$\displaystyle 1.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} x^2+1, & \text{ja} & x\leq 1, \\ x-1, & \text{ja} & x>1; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{2}{x}, & \text{ja} & x<0... ... x<\frac{\pi}{2}, \\ 0, & \text{ja} & x\geq\frac{\pi}{2}; \\ \end{array}\right.$
$\displaystyle 2.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} x^2+1, & \text{ja} & x<1, \\ \frac{1}{x-1}, & \text{ja} & x>1; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \lg(1-x), & \text{ja} & x<1, \... ...\text{ja} & 1\leq x<2, \\ 3^{x-2}, & \text{ja} & x\geq 2; \\ \end{array}\right.$
$\displaystyle 3.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} x^2+1, & \text{ja} & x<1, \\ 3, & \text{ja} & x=1, \\ x+1, & \text{ja} & x>1; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} -\frac{8}{x}, & \text{ja} & x<... ...text{ja} & 0\leq x\leq 2, \\ \ln(x-2), & \text{ja} & x>2; \\ \end{array}\right.$
$\displaystyle 4.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{1}{x+1}, & \text{ja} & x<3, \\ 0, & \text{ja} & x=3, \\ \ln(x-3), & \text{ja} & x>3; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{x^3-1}{x-1}, & \text{ja} & x\neq 1, \\ 3, & \text{ja} & x=1; \\ \end{array}\right.$
$\displaystyle 5.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} x^2-2, & \text{ja} & x<1, \\ -... ...ja} & 1\leq x<4, \\ \frac{1}{x-6}, & \text{ja} & x\geq 4; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} (x+1)^2, & \text{ja} & x\leq 0, \\ \ln x, & \text{ja} & x>0; \\ \end{array}\right.$
$\displaystyle 6.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} 3^{x-2}, & \text{ja} & x<2, \\ x, & \text{ja} & 2\leq x<4, \\ \ln(x-4), & \text{ja} & x>4; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{25-x^2}{x-5}, & \text{ja} & x\neq 5, \\ -10, & \text{ja} & x=5; \\ \end{array}\right.$
$\displaystyle 7.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} -8^{1-x}, & \text{ja} & x<1, \\ 0, & \text{ja} & x=1, \\ \frac{1}{x-3}, & \text{ja} & x>1; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \lg x, & \text{ja} & x>0, \\ 1-x^2, & \text{ja} & x\leq 0; \\ \end{array}\right.$
$\displaystyle 8.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \tg x, & \text{ja} & \vert x\v... ...rac{1}{x^2}, & \text{ja} & \vert x\vert\geq\frac{\pi}{2}; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \sqrt{-x}, & \text{ja} & x<0, \\ e^x, & \text{ja} & x\geq 0; \\ \end{array}\right.$
$\displaystyle 9.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{8-x^3}{x-2}, & \text{ja} & x\neq 2, \\ 0, & \text{ja} & x=2; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} -\frac{2}{x}, & \text{ja} & x<... ...text{ja} & 1\leq x\leq 3, \\ \lg(x-3), & \text{ja} & x>3; \\ \end{array}\right.$
$\displaystyle 10.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} x, & \text{ja} & x\leq 0, \\ 1... ...ext{ja} & 0<x\leq 1, \\ \frac{1}{1-x}, & \text{ja} & x>1; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} -\frac{9-x^2}{x+3}, & \text{ja} & x\neq -3, \\ 0, & \text{ja} & x=-3; \\ \end{array}\right.$
$\displaystyle 11.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} x^2, & \text{ja} & x<-1, \\ 1, & \text{ja} & x=-1, \\ \frac{1}{x+1}, & \text{ja} & x>-1; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{1}{2}, & \text{ja} & x<-... ...ja} & \vert x\vert\leq 1, \\ \lg(x-1), & \text{ja} & x>1; \\ \end{array}\right.$
$\displaystyle 12.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{x^2-1}{x-1}, & \text{ja} & x<1, \\ 5, & \text{ja} & x=1; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \tg x, & \text{ja} & \vert x\v... ...\leq -\frac{\pi}{2}, \\ 1, & \text{ja} & x>\frac{\pi}{2}; \\ \end{array}\right.$
$\displaystyle 13.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} x^2+1, & \text{ja} & x<-2, \\ ... ...& \text{ja} & -2\leq x<2, \\ 3x+2, & \text{ja} & x\geq 2; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \sqrt{2-x}, & \text{ja} & x\leq 2, \\ \ln(x^2-4), & \text{ja} & x>2; \\ \end{array}\right.$
$\displaystyle 14.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} x+2, & \text{ja} & x<0, \\ 0, & \text{ja} & x=0, \\ 3-x^2, & \text{ja} & x>0; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \ln(2-x), & \text{ja} & x<2, \... ...xt{ja} & 2\leq x<3, \\ \sqrt{x-3}, & \text{ja} & x\geq 3; \\ \end{array}\right.$
$\displaystyle 15.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} x^3+1, & \text{ja} & x\leq 0, \\ \ln x, & \text{ja} & x>0; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{16-x^2}{x+4}, & \text{ja} & x\neq -4, \\ 1, & \text{ja} & x=-4; \\ \end{array}\right.$
$\displaystyle 16.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} e^x, & \text{ja} & x<0, \\ \sq... ...x}, & \text{ja} & 0\leq x<3, \\ x^2-5, & \text{ja} & x>3; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{1}{x+1}, & \text{ja} & x... ...ja} & \vert x\vert\leq 1, \\ \lg(x-1), & \text{ja} & x>1; \\ \end{array}\right.$
$\displaystyle 17.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{3}{x}, & \text{ja} & x\leq 3, \\ \ln(x-3), & \text{ja} & x>3; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} x^2+2x, & \text{ja} & x<0, \\ ... ... \text{ja} & 0<x<1, \\ \sqrt{x-1}, & \text{ja} & x\geq 1; \\ \end{array}\right.$
$\displaystyle 18.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} x^2+3, & \text{ja} & x<0, \\ 3, & \text{ja} & x=0, \\ 4-x, & \text{ja} & x>0; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{1}{2-x}, & \text{ja} & x... ...ext{ja} & 0<x\leq 2, \\ \sqrt{-x}, & \text{ja} & x\leq 0; \\ \end{array}\right.$
$\displaystyle 19.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} -\frac{1}{2}-x, & \text{ja} & ... ...c{\pi}{2}<x\leq 0, \\ x^2+\frac{1}{2}, & \text{ja} & x>0; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{x^3-8}{2-x}, & \text{ja} & x\neq 2, \\ 0, & \text{ja} & x=2; \\ \end{array}\right.$
$\displaystyle 20.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \sin x, & \text{ja} & \vert x\... ...\\ \frac{1}{2}, & \text{ja} & \vert x\vert>\frac{\pi}{2}; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{4}{x}, & \text{ja} & x\l... ...ext{ja} & -2\leq x\leq 1, \\ \ln(x-1), & \text{ja} & x>1; \\ \end{array}\right.$
$\displaystyle 21.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{1}{1-x}, & \text{ja} & x... ... x^2-4, & \text{ja} & 1<x\leq 3, \\ 5, & \text{ja} & x>3; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{x^2-36}{x+6}, & \text{ja} & x\neq -6, \\ 10, & \text{ja} & -2\leq x=-6; \\ \end{array}\right.$
$\displaystyle 22.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} 3, & \text{ja} & x<-2, \\ x^2-1, & \text{ja} & -2\leq x<2, \\ x+4, & \text{ja} & x\geq 2; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \sqrt{1-x}, & \text{ja} & x\le... ... & \text{ja} & 1<x\leq 3, \\ \lg(x-3), & \text{ja} & x>3; \\ \end{array}\right.$
$\displaystyle 23.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} 5-x, & \text{ja} & x<-1, \\ x^2+3, & \text{ja} & -1\leq x<2, \\ 7, & \text{ja} & x\geq 2; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \frac{1}{5+x}, & \text{ja} & x<-1, \\ 2, & \text{ja} & x=1, \\ 1-x^2, & \text{ja} & x<1; \\ \end{array}\right.$
$\displaystyle 24.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} x-1, & \text{ja} & x<-2, \\ 4-x^2, & \text{ja} & -2\leq x<1, \\ 3, & \text{ja} & x\geq 1; \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \ln(5-x), & \text{ja} & x<5, \... ...\text{ja} & 5\leq x<6, \\ 2^{x-6}, & \text{ja} & x\geq 6; \\ \end{array}\right.$
$\displaystyle 25.\;a)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} -x-11, & \text{ja} & x<-2, \\ ... ...& \text{ja} & -2\leq x<2, \\ x-11, & \text{ja} & x\geq 2. \\ \end{array}\right.$
$\displaystyle b)$	$\displaystyle \;\;f(x)=\left\{\begin{array}{ccc} \tg x, & \text{ja} & \vert x\v... ...leq -\frac{\pi}{2}, \\ -x, & \text{ja} & x>\frac{\pi}{2}; \\ \end{array}\right.$