Đáp án:
$\begin{array}{l}
a)\lim \dfrac{{{{4.3}^n} + {7^{n + 1}}}}{{{{2.5}^n} + {7^n}}} = \lim \dfrac{{4.\dfrac{{{3^n}}}{{{7^n}}} + 7}}{{2.\dfrac{{{5^n}}}{{{7^n}}} + 1}} = \dfrac{7}{1} = 7\\
b)\mathop {\lim }\limits_{x \to 2} \dfrac{{2 - x}}{{\sqrt {x + 7} - 3}}\\
= \mathop {\lim }\limits_{x \to 2} \dfrac{{\left( {2 - x} \right)\left( {\sqrt {x + 7} + 3} \right)}}{{x + 7 - 9}}\\
= \mathop {\lim }\limits_{x \to 2} \left( { - \sqrt {x + 7} - 3} \right)\\
= - \sqrt {2 + 7} - 3\\
= - 6
\end{array}$
