Question

$\displaystyle \lim_{x \to 0}$ $\frac{\left(1+2x\right)^{10}-1}{x}$ is equal to

• A. $5$
• B. $10$
• C. $15$
• D. $20$

Answer 1

Answer: (D)

$20$

Answer 2

$\displaystyle\lim _{x \rightarrow 0} \frac{(1+2 x)^{10}-1}{x}$ $(\frac{0}{0}$ form )
Using L' hospital rule,
$=\displaystyle\lim _{x \rightarrow 0} \frac{10(1+2 x)^{9}(2)-0}{1}$
$=10(1+0)^{9} \cdot 2=20$