Tìm các giới han sau:a) \(\mathop {\lim }\limits_{x \to  - 1} \left( { - 5{x^2} + 7x - 4} \right)\)b) \(\mathop {\lim }\limits_{x \t

* Hướng dẫn giải

a) \(\mathop {\lim }\limits_{x \to  - 1} \left( { - 5{x^2} + 7x - 4} \right)=-16\)

b) \(\mathop {\lim }\limits_{x \to 3} \frac{{9 - {x^2}}}{{\sqrt {x + 6}  - 3}} = \mathop {\lim }\limits_{x \to 3} \frac{{(3 - x)(3 + x)\left( {\sqrt {x + 6}  + 3} \right)}}{{x - 3}}\)

\(=\mathop {\lim }\limits_{x \to 3} \left[ {( - 3 - x)\left( {\sqrt {x + 6}  + 3} \right)} \right]\,\, = \,\, - 6.6\,\, = \,\, - 36\)

c) \(\mathop {\lim }\limits_{x \to  + \infty } \left( {\sqrt {{x^2} + x}  - x} \right) = \mathop {\lim }\limits_{x \to  + \infty } \frac{{{x^2} + x - {x^2}}}{{\sqrt {{x^2} + x}  + x}} = \frac{1}{2}\)