Question

$\underset{x\to 0}{Lt}\frac{\sqrt[5]{52+x}-\sqrt[5]{52-x}}{\sin hx}=$

• A. $0$
• B. $\sqrt[5]{52}$
• C. $\sqrt{5}/2$
• D. $\sqrt[5]{52}/5$

Answer 1

The correct option is A $0$

$\underset{x\to 0}{lt}\frac{\sqrt[5]{52+x}-\sqrt[5]{52-x}}{\sin hx}$

$=\underset{x\to 0}{lt}\frac{\sqrt[5]{52+x}-\sqrt[5]{52-x}}{(e^x-e^{-x})/2}$

$=\frac{\sqrt[5]{52}-\sqrt[5]{52}}{\left(\frac{1-1}{2}\right)}=0$.