Find the limit exactly (Hint: multiply and divide by the conjugate expression and simplify).
A) 4
B) -4
C) 0
D) the limit does not exist

Question

Find the limit exactly (Hint: multiply and divide by the conjugate expression and simplify). 
A) 4 
B) -4 
C) 0 
D) the limit does not exist

Quizplus · Accepted Answer

We can simplify the expression by multiplying the numerator and denominator by the conjugate expression, which is $\sqrt{x+4}+2$. This gives us:
$$
\lim_{x	o -4} \frac{(2+\sqrt{x+4})(\sqrt{x+4}-2)}{(x+4)-4} = \lim_{x	o -4} \frac{(x+4)-4}{(\sqrt{x+4}-2)(\sqrt{x+4}+2)} = \frac{0}{-4} = 0
$$
Therefore, the limit is 0.

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