Question

${\lim }_{x\to 0}\frac{\sqrt{1+2x-1}}{x}=$

• A. 0
• B. -1
• C. $\frac{1}{2}$
• D. 1
• E. $\frac{-1}{2}$

Answer 1

Answer: (D)

$\underset{x\to 0}{\lim }\frac{\sqrt{1+2x}-1}{x}$
Using L' Hospital's Rule,
$\underset{x\to 0}{\lim }\frac{\frac{1}{2\sqrt{1+2x}}\cdot 2-0}{1}$
$\Rightarrow \underset{x\to 0}{\lim }\frac{1}{\sqrt{1+2x}}$
Using limit, we get
$=\frac{1}{\sqrt{1+2(0)}}=1$