Find the limit exactly (Hint: multiply and divide by the conjugate expression and simplify).
A) 6
B) -6
C) 0
D) the limit does not exist

Question

Find the limit exactly (Hint: multiply and divide by the conjugate expression and simplify). 
A) 6 
B) -6 
C) 0 
D) the limit does not exist

Quizplus · Accepted Answer

To find the limit of the given expression, we need to use the conjugate expression and simplify as follows:
$\lim_{x 	o -1} \frac{\sqrt{x+2}-3}{x+1} = \lim_{x 	o -1} \frac{\sqrt{x+2}-3}{x+1} \cdot \frac{\sqrt{x+2}+3}{\sqrt{x+2}+3}$
$= \lim_{x 	o -1} \frac{(x+2)-9}{(x+1)(\sqrt{x+2}+3)} = \lim_{x 	o -1} \frac{-(x+1)}{\sqrt{x+2}+3} = \frac{-2}{0+3} = 0$
Therefore, the limit is 0, which is choice C.

Find the Limit Exactly (Hint: Multiply and Divide by the Conjugate