a)  $\underset{x\to -1}{\lim }\left(x^3-3x\right);$                  b)       $\underset{x\to 2}{\lim }\sqrt{2x+5};$                  c)$\underset{x\to +\infty }{\lim }\frac{4-x}{2x+1}.$

a) $\underset{x\to -3}{\lim }\left(8+3x-x^2\right);$                                 b)$\underset{x\to 2}{\lim }\left[\left(5x-1\right)\left(2-4x\right)\right];$

c)$\underset{x\to -2}{\lim }\frac{x^2-x}{{\left(2x+1\right)}^2};$                                       d)$\underset{x\to -1}{\lim }\sqrt{10-2x^2}.$

a)     $\underset{x\to -2}{\lim }\frac{x^2-4}{x+2};$                                     b) $\underset{x\to 1}{\lim }\frac{x^3-1}{1-x};$

c)  $\underset{x\to 3}{\lim }\frac{x^2-4x+3}{x-3};$                                  d)$\underset{x\to -2}{\lim }\frac{2-\sqrt{x+6}}{x+2};$

e)   $\underset{x\to 0}{\lim }\frac{x}{\sqrt{x+1}-1};$                                  g)$\underset{x\to 2}{\lim }\frac{x^2-4x+4}{x^2-4}.$

a)$\underset{x\to 4}{\lim }\left[g\left(x\right)-3f\left(x\right)\right];$                             b)$\underset{x\to 4}{\lim }\frac{2f\left(x\right)\cdot g\left(x\right)}{{\left[f\left(x\right)+g\left(x\right)\right]}^2}.$

a) $\underset{x\to 0}{\lim }\frac{x^2}{\left|x\right|};$                                                 b)$\underset{x\to 2}{\lim }\frac{x^2-2x}{\left|x-2\right|}.$

a)  $\underset{x\to +\infty }{\lim }\frac{x}{x+4};$                                         b)$\underset{x\to -\infty }{\lim }\frac{2x^2+1}{{\left(2x+1\right)}^2};$

c)     $\underset{x\to -\infty }{\lim }\frac{3x+1}{\sqrt{x^2-2x}};$                                d)$\underset{x\to +\infty }{\lim }\left(x-\sqrt{x^2+2x}\right).$

a)$\underset{x\to -\infty }{\lim }\left(x^3+2x^2-1\right);$                b) $\underset{x\to +\infty }{\lim }\frac{x^3+2x^2}{3x^2+1};$                       c)$\underset{x\to -\infty }{\lim }\sqrt{x^2-2x+3}.$

a)    $\underset{x\to 2}{\lim }\frac{ax+b}{x-2}=5;$                                 b)$\underset{x\to 1}{\lim }\frac{a\sqrt{x}+b}{x-1}=3.$