Question

Find the limit ;-
$\underset{x\to -1}{lim}\frac{x^2+x-2}{\left(x^2+x\right)+\sin \left(x+1\right)}$

Answer 1

${lim}_{x\to -1}$ $\frac{x^2-x-2}{(x^2+x)+sin(x+1)}$

apply L-Hospital rule

${lim}_{x\to -1}$ $\frac{2x-1}{2x+1+cos(x+1)}$

${lim}_{x\to -1}$ $\frac{-2-1}{-2+1+1}$=$\frac{-3}{0}$

limit does not exist