Question

$\underset{x\to 0}{lim}\frac{(1+x{)}^5-1}{(1+x{)}^3-1}=$

• A. $0$
• B. $1$
• C. $\frac{5}{3}$
• D. none

Answer 1

Answer: (C)

$\frac{5}{3}$

$={lim}_{x\to 0}\frac{{(1+x)}^5-1}{{(1+x)}^3-1}$ (of the form $\frac{0}{0}$)

$l={lim}_{x\to 0}\frac{5{(1+x)}^4}{3{(1+x)}^2}$ (L-Hoapital rule)

$l=\frac{5}{3}$