2.1 Q-11

Q11. ${\lim }_{x\to -3}\frac{2x+6}{4x^2-36}$

\section*{Solution:} ${\lim }_{x\to -3}\frac{2x+6}{4x^2-36}$ $\begin{array}{rl}& =\underset{x\to -3}{\lim }\frac{{}^{1}2(x+3)}{2A\left(x^2-9\right)}\\ & =\underset{x\to -3}{\lim }\frac{(x+3)}{2\left((x{)}^2-(3{)}^2\right)}\\ & =\underset{x\to -3}{\lim }\frac{x+3}{2(x-3)(x+3)}\\ & =\underset{x\to -3}{\lim }\frac{1}{2(x-3)}\\ & =\frac{1}{2(-3-3)}\\ & =\frac{1}{2(-6)}=\frac{-1}{12}\end{array}$