Question

$\underset{x\to -5}{\lim }\frac{2x^2+9x-5}{x+5}$

Answer 1

$$\begin{gathered} \underset{x\to -5}{\lim }\left[\frac{2x^2+9x-5}{x+5}\right] \\ \mathrm{It}\mathrm{is}\mathrm{of}\mathrm{the}\mathrm{form}\frac{0}{0}. \\ \underset{x\to -5}{\lim }\left[\frac{2x^2+10x-x-5}{x+5}\right] \\ =\underset{x\to -5}{\lim }\left[\frac{2x\left(x+5\right)-1\left(x+5\right)}{x+5}\right] \\ =\underset{x\to -5}{\lim }\left[\frac{\left(2x-1\right)\left(x+5\right)}{x+5}\right] \\ =\underset{x\to -5}{\lim }\left(2x-1\right) \\ =2\left(-5\right)-1 \\ =-11 \end{gathered}$$