Giải thích các bước giải:
\(\begin{array}{l}
c,\\
\mathop {\lim }\limits_{x \to 2} \frac{{\sqrt {x + 2} - 2}}{{\sqrt {x + 7} - 3}}\\
= \mathop {\lim }\limits_{x \to 2} \left[ {\frac{{x + 2 - {2^2}}}{{\sqrt {x + 2} + 2}}:\frac{{x + 7 - {3^2}}}{{\sqrt {x + 7} + 3}}} \right]\\
= \mathop {\lim }\limits_{x \to 2} \left[ {\frac{{x - 2}}{{\sqrt {x + 2} + 2}}:\frac{{x - 2}}{{\sqrt {x + 7} + 3}}} \right]\\
= \mathop {\lim }\limits_{x \to 2} \frac{{\sqrt {x + 7} + 3}}{{\sqrt {x + 2} + 2}}\\
= \frac{{\sqrt {2 + 7} + 3}}{{\sqrt {2 + 2} + 2}}\\
= \frac{6}{4} = \frac{3}{2}\\
i,\\
\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {x + 9} + \sqrt {x + 16} - 7}}{x}\\
= \mathop {\lim }\limits_{x \to 0} \frac{{\left( {\sqrt {x + 9} - 3} \right) + \left( {\sqrt {x + 16} - 4} \right)}}{x}\\
= \mathop {\lim }\limits_{x \to 0} \frac{{\frac{{x + 9 - {3^2}}}{{\sqrt {x + 9} + 3}} + \frac{{x + 16 - {4^2}}}{{\sqrt {x + 16} + 4}}}}{x}\\
= \mathop {\lim }\limits_{x \to 0} \frac{{\frac{x}{{\sqrt {x + 9} + 3}} + \frac{x}{{\sqrt {x + 16} + 4}}}}{x}\\
= \mathop {\lim }\limits_{x \to 0} \left[ {\frac{1}{{\sqrt {x + 9} + 3}} + \frac{1}{{\sqrt {x + 16} + 4}}} \right]\\
= \frac{1}{{\sqrt {0 + 9} + 3}} + \frac{1}{{\sqrt {0 + 16} + 4}}\\
= \frac{1}{6} + \frac{1}{8} = \frac{7}{{24}}
\end{array}\)
