Question

$\underset{x\to 1}{lim}\frac{1-x^{-2/3}}{1-x^{-1/3}}$ is equal to

• A. 2
• B. 1
• C. $\frac{2}{3}$
• D. none of these

Answer 1

Answer: (A)

2

We have,
$\underset{x\to 1}{lim}\frac{1-x^{-2/3}}{1-x^{-1/3}}$
$=\underset{x\to 1}{lim}\frac{1^2-(x^{-1/3}{)}^2}{1-x^{-1/3}}$
$=\underset{x\to 1}{lim}\frac{(1+x^{-1/3})(1-x^{-1/3})}{1-x^{-1/3}}$
$={lim}_{x\to 1}1+x^{-1/3}=1+1=2$
Hence, option 'A' is correct.