Find the limit, if it exists.
-$$\lim _ { x \rightarrow 0 } \frac { \sqrt { 1 + x } - 1 } { x }$$
A) Does not exist
B) $1 / 2$
C) 0
D) $1 / 4$

Question

Quizplus · Accepted Answer

We can rewrite the expression as: 
\begin{align*} 
\lim_{x ightarrow 0} \frac{\sqrt{1+x} -1}{x} &= \lim_{x ightarrow 0} \frac{\sqrt{1+x} -1}{x} \cdot \frac{\sqrt{1+x}+1}{\sqrt{1+x}+1} \ 
&= \lim_{x ightarrow 0} \frac{1}{\sqrt{1+x}+1} \
&= 1/2. 
\end{align*}
Therefore, the limit is 1/2, which corresponds to choice B.

Find the Limit, If It Exists lim⁡x→01+x−1x\lim _ { x \rightarrow 0 } \frac { \sqrt { 1 + x } - 1 } { x }x→0lim​x1+x​−1​

Find the Limit, If It Exists $\lim _ { x \rightarrow 0 } \frac { \sqrt { 1 + x } - 1 } { x }$