# Use the conjugate process lim_(x->0) (sqrt(x^2+5)-sqrt(5-x^2))/x.

Use the conjugate process $\underset{x\to 0}{lim}\frac{\sqrt{{x}^{2}+5}-\sqrt{5-{x}^{2}}}{x}.$
You can still ask an expert for help

## Want to know more about Limits and continuity?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

cheekabooy
The expression simplifies:
$\frac{\sqrt{5}\cdot \sqrt{1+\frac{{x}^{2}}{5}}-\sqrt{5}\cdot \sqrt{1-\frac{{x}^{2}}{5}}}{x}=$
$\sqrt{5}\frac{\frac{{\left(1+\frac{{x}^{2}}{5}\right)}^{1}}{2}-\frac{{\left(1-\frac{{x}^{2}}{5}\right)}^{1}}{2}}{x}$
$⇒\sqrt{5}\frac{\left(1+\frac{{x}^{2}}{10}\right)-\left(1-\frac{{x}^{2}}{10}\right)}{x}=$
$\sqrt{5}\frac{2\frac{{x}^{2}}{10}}{x}=\sqrt{5}\frac{x}{5}$