## Problem Statement

Calculate the limit of the function:
$\lim _{x \rightarrow 3} \frac{x^{3}-4 x^{2}-3 x+18}{x^{3}-5 x^{2}+3 x+9}$
## Solution

$\lim _{x \rightarrow 3} \frac{x^{3}-4 x^{2}-3 x+18}{x^{3}-5 x^{2}+3 x+9}=\left\{\frac{0}{0}\right\}=\lim _{x \rightarrow 3} \frac{(x-3)\left(x^{2}-x-6\right)}{(x-3)\left(x^{2}-2 x-3\right)}=$

$=\lim _{x \rightarrow 3} \frac{x^{2}-x-6}{x^{2}-2 x-3}=\left\{\frac{0}{0}\right\}=\lim _{x \rightarrow 3} \frac{(x-3)(x+2)}{(x-3)(x+1)}=$

$=\lim _{x \rightarrow 3} \frac{x+2}{x+1}=\frac{3+2}{3+1}=\frac{5}{4}=1 \frac{1}{4}$

## Problem Kuznetsov Limits 10-31