Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {x + 9} + \sqrt {x + 16} - 7}}{x}\\
= \mathop {\lim }\limits_{x \to 0} \frac{{\left( {\sqrt {x + 9} - 3} \right) + \left( {\sqrt {x + 16} - 4} \right)}}{x}\\
= \mathop {\lim }\limits_{x \to 0} \frac{{\frac{{x + 9 - 9}}{{\sqrt {x + 9} + 3}} + \frac{{x + 16 - 16}}{{\sqrt {x + 16} + 4}}}}{x}\\
= \mathop {\lim }\limits_{x \to 0} \frac{{\frac{x}{{\sqrt {x + 9} + 3}} + \frac{x}{{\sqrt {x + 16} + 4}}}}{x}\\
= \mathop {\lim }\limits_{x \to 0} \left( {\frac{1}{{\sqrt {x + 9} + 3}} + \frac{1}{{\sqrt {x + 16} + 4}}} \right)\\
= \frac{1}{{\sqrt {0 + 9} + 3}} + \frac{1}{{\sqrt {0 + 16} + 4}}\\
= \frac{1}{{3 + 3}} + \frac{1}{{4 + 4}}\\
= \frac{7}{{24}}
\end{array}\)
