الف) $\mathop {\lim }\limits_{x \to 1} \frac{{\left( {x - \sqrt x } \right)\left( {x + \sqrt x } \right)}}{{\left( {x - 1} \right)\left( {x + 2} \right)\left( {x + \sqrt x } \right)}} $

$= \mathop {\lim }\limits_{x \to 1} \frac{{x\left( {x - 1} \right)}}{{\left( {x - 1} \right)\left( {x + 2} \right)\left( {x + \sqrt x } \right)}} = \frac{1}{6}$

ب) $\mathop {\lim }\limits_{x \to {{\frac{\pi }{2}}^ + }} \frac{{\sin x}}{{\cos x}} = \frac{1}{{{0^ - }}} =  - \infty $

ج) $\mathop {\lim }\limits_{x \to  - \infty } \frac{{{x^7}( - 4 + \frac{5}{{{x^5}}})}}{{{x^3}(2 + \frac{9}{{{x^3}}})}} $

$= \mathop {\lim }\limits_{x \to  - \infty } ( - 2){x^4} =  - \infty $