question evaluate the limit: $lim_{x\rightarrow - 7}\frac{x + 7}{sqrt{x + 11}-2}$ answer dne
question evaluate the limit: $lim_{x\rightarrow - 7}\frac{x + 7}{sqrt{x + 11}-2}$ answer dne
Answer
Answer:
4
Explanation:
Step1: Rationalize the denominator
Multiply the numerator and denominator by $\sqrt{x + 11}+2$. [ \begin{align*} &\lim_{x\rightarrow - 7}\frac{x + 7}{\sqrt{x + 11}-2}\times\frac{\sqrt{x + 11}+2}{\sqrt{x + 11}+2}\ =&\lim_{x\rightarrow - 7}\frac{(x + 7)(\sqrt{x + 11}+2)}{(x + 11)-4}\ =&\lim_{x\rightarrow - 7}\frac{(x + 7)(\sqrt{x + 11}+2)}{x+7} \end{align*} ]
Step2: Simplify the expression
Cancel out the common factor $(x + 7)$ (since $x\neq - 7$ when taking the limit). [ \lim_{x\rightarrow - 7}(\sqrt{x + 11}+2) ]
Step3: Substitute $x=-7$
[ \sqrt{-7 + 11}+2=\sqrt{4}+2=2 + 2=4 ]