$\mathop {\lim }\limits_{x \to 3} {\left( {3 - 4x} \right)^2}$         

$\mathop {\lim }\limits_{x \to  - 1} {{{x^2} + x + 1} \over {2{x^5} + 3}}$

$\mathop {\lim }\limits_{x \to 1} {{{x^2}\left( {2x - 1} \right)} \over {{x^4} + x + 1}}$  

$\mathop {\lim }\limits_{x \to 2} \root 3 \of {{{{x^2} - x + 1} \over {{x^2} + 2x}}}$

$\mathop {\lim }\limits_{x \to 3} \sqrt {{{9{x^2} - x} \over {\left( {2x - 1} \right)\left( {{x^4} - 3} \right)}}}$      

$\mathop {\lim }\limits_{x \to 0} {{1 - {1 \over x}} \over {1 + {1 \over x}}}$

$\mathop {\lim }\limits_{x \to  + \infty } \left| {{{ - {x^2} - x + 6} \over {{x^2} + 3x}}} \right|$       

$\mathop {\lim }\limits_{x \to  - 2} {{{{\left( {{x^2} - x + 6} \right)}^2}} \over {{x^3} + 2{x^2}}}$