Đáp án:
Giải thích các bước giải:
Câu 3:
\(\begin{array}{l}
a.\mathop {\lim }\limits_{x \to 0} \frac{{2x\left( {\sqrt {x + 9} + 3} \right)}}{{{{\left( {\sqrt {x + 9} } \right)}^2} - {3^2}}} = \mathop {\lim }\limits_{x \to 0} \frac{{2x\left( {\sqrt {x + 9} + 3} \right)}}{{x + 9 - 9}}\\
= \mathop {\lim }\limits_{x \to 0} \frac{{2x\left( {\sqrt {x + 9} + 3} \right)}}{x} = \mathop {\lim }\limits_{x \to 0} 2\left( {\sqrt {x + 9} + 3} \right) = 12\\
b.\mathop {\lim }\limits_{x \to 1} \frac{{x + 3 - 4}}{{2(x - 1)(x + 1)\left( {\sqrt {x + 3} + 2} \right)}} = \mathop {\lim }\limits_{x \to 1} \frac{{x - 1}}{{2(x - 1)(x + 1)\left( {\sqrt {x + 3} + 2} \right)}}\\
= \mathop {\lim }\limits_{x \to 1} \frac{1}{{2(x + 1)\left( {\sqrt {x + 3} + 2} \right)}} = \frac{1}{{16}}
\end{array}\)
