Question

Evaluate: $\underset{x\to 20}{lim}\frac{\sqrt{x+5}+5}{\sqrt{x+5}-5}$

• A. 1
• B. 2
• C. 4
• D. $\infty$

Answer 1

The correct option is D $\infty$

Given,
$\underset{x\to 20}{lim}\frac{\sqrt{x+5}+5}{\sqrt{x+5}-5}=\underset{x\to 20}{lim}\frac{(\sqrt{x+5}+5)(\sqrt{x+5}-5)}{(\sqrt{x+5}-5)(\sqrt{x+5}-5)}=\underset{x\to 20}{lim}\frac{(x+5-25)}{(x+5)+25-10\sqrt{x+5}}=\underset{x\to 20}{lim}\frac{(x-20)}{x+30-10\sqrt{x+5}}$
Substituting $x=20$, we get
$=\frac{(20-20)}{20+30-10\sqrt{20+5}}=\frac{0}{50-50}=\frac{0}{0}=\infty$