Question

$\underset{h\to 0}{lim}\{\frac{1}{h\sqrt[3]{38+h}}-\frac{1}{2h}\}\text{is equal to}$

• A. 1/2
• B. -4/3
• C. -16/3
• D. -1/48

Answer 1

The correct option is D

-1/48

$\underset{h\to 0}{lim}\frac{2-\sqrt[3]{38+h}}{\sqrt[3]{38+h}}\text{limit}=\underset{h\to 0}{lim}\frac{8-(8+h)}{2h\sqrt[3]{38+h}\{8^{2/3}+8^{1/3}(8+h{)}^{1/3}+(8+h{)}^2/3\}}=-\frac{1}{48}$