124. Find $\lim _{x \rightarrow-2} \frac{2 x^{2}+7 x+6}{(x+2)^{2}}$.
Solution. Direct substitution $x=-2$ shows that there is an indeterminate form of $0 / 0$. By factoring the numerator and simplifying the fraction, we find

$$
\lim _{x \rightarrow-2} \frac{2 x^{2}+7 x+6}{(x+2)^{2}}=\lim _{x \rightarrow-2} \frac{2(x+2)\left(x+\frac{3}{2}\right)}{(x+2)^{2}}=\lim _{x \rightarrow-2} \frac{2 x+3}{x+2}
$$

Here the limit of the denominator is zero. Thus, the denominator of the fraction decreases without bound and approaches zero, while the numerator approaches -1. It is clear that the entire fraction grows without bound, which is conditionally written as: $\lim _{x \rightarrow-2} \frac{2 x^{2}+7 x+6}{(x+2)^{2}}=\infty$.

125-130. Find the limits: