Question

Evaluate: $\underset{x\to 0}{lim}\frac{(1+x{)}^4-1}{(1+x{)}^3-1}$

• A. $-\frac{4}{3}$
• B. $0$
• C. $\frac{4}{3}$
• D. $\frac{3}{4}$

Answer 1

Answer: (C)

$\frac{4}{3}$

${lim}_{x\to 0}\frac{{(1+x)}^4-1}{{(1+x)}^3-1}$

Since $\frac{x^m-a^m}{x^n-a^n}=\frac{m}{n}{a}^{m-n}$, we have

$m=4,n=3$ from the given equation.

Thus, ${lim}_{x\to 0}\frac{{(1+x)}^4-1}{{(1+x)}^3-1}$

$=\frac{4}{3}(1{)}^{4-3}$

$=\frac{4}{3}$