Question

Solve:

$\underset{x\to 2}{Lt}\frac{x^{\sqrt{2}}-2^{\sqrt{2}}}{x-2}=$

• A. $\sqrt{2}{.2}^{\sqrt{2}}$
• B. $2^{\sqrt{2}-1}$
• C. $2^{\sqrt{2}-\frac{1}{2}}$
• D. $2^{\sqrt{2}}$

Answer 1

The correct option is C $2^{\sqrt{2}-\frac{1}{2}}$

$\underset{x\to 2}{Lt}\frac{x^{\sqrt{2}}-2^{\sqrt{2}}}{x-2}\Rightarrow$

L' Hospital -

$\underset{x\to 2}{Lt}\frac{\sqrt{2}.x^{\sqrt{2}-1}}{1}$

$=\sqrt{2}\times (2{)}^{\sqrt{2}-1}$

$=\frac{\sqrt{2}\times 2^{\sqrt{2}}}{2}$

$=(2{)}^{\sqrt{2}-\frac{1}{2}}$