Find the limit exactly (Hint: multiply and divide by the conjugate expression and simplify).
C) 5
D) The limit does not exist.

Question

Find the limit exactly (Hint: multiply and divide by the conjugate expression and simplify). 
C) 5 
D) The limit does not exist.

Quizplus · Accepted Answer

Multiplying and dividing by the conjugate expression, we get:
$\lim_{x	o 0}\frac{1-\sqrt{1+x}}{x} \cdot \frac{1+\sqrt{1+x}}{1+\sqrt{1+x}} = \lim_{x	o 0}\frac{1-(1+x)}{x(1+\sqrt{1+x})} = \lim_{x	o 0}\frac{-x}{x(1+\sqrt{1+x})} = \lim_{x	o 0}\frac{-1}{1+\sqrt{1+x}} = -\frac{1}{2}$
Therefore, the correct answer is B.

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