Question

Solve: $\underset{x\to 1}{lim}\frac{x^2-\sqrt{x}}{\sqrt{x}-1}$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (C)

$3$

$\underset{x\to 1}{lim}\frac{x^2-\sqrt{x}}{\sqrt{x}-1}$ $=\underset{x\to 1}{lim}\frac{x^{1/2}(x^{3/2}-1)}{\sqrt{x}-1}$

$=\underset{x\to 1}{lim}\frac{x^{1/2}(x^{3/2}-1)}{x-1}$

$=\underset{x\to 1}{lim}\frac{x-1}{\sqrt{x}-1}$

$=\frac{3}{2}\times \frac{1}{\frac{1}{2}}$ ..... $(\because \underset{x\to a}{lim}\frac{x^n-a^n}{x-a}=n{a}^{n-1})$
$=3$