Question

The value of $\underset{x\to \infty }{lim}\sqrt{x}(\sqrt{x+c}-\sqrt{x})is:$

• A. c/2
• B. c/3
• C. c/4
• D. c

Answer 1

The correct option is A

c/2

$\underset{x\to \infty }{lim}\sqrt{x}(\sqrt{x+c}-\sqrt{x})\underset{x\to \infty }{lim}\frac{\sqrt{x}(\sqrt{x+c}-\sqrt{x})(\sqrt{x+c}+\sqrt{x})}{(\sqrt{x+c}+\sqrt{x})}\underset{x\to \infty }{lim}\frac{c}{\sqrt{1+\frac{c}{x}}+1}=\frac{c}{2}$