Question

${lim}_{x\to 1}\frac{1-x^{1/3}}{1-x^{1/4}}=$___

• A. $1$
• B. $\frac{4}{3}$
• C. $\frac{3}{4}$
• D. $0$

Answer 1

The correct option is B $\frac{4}{3}$

$letx=t^{12}whenx\to 1,t\to 1{lim}_{t\to 1}\frac{1-t^{\frac{12}{3}}}{1-t^{\frac{12}{4}}}\frac{1-t^4}{1-t^3}\Rightarrow \frac{t^4-1}{t^3-1}\Rightarrow \frac{(t-1)(t+1)(t^2+1)}{(t-1)(t^2+t+1)}\Rightarrow \frac{2\times 2}{3}\Rightarrow \frac{4}{3}$