Question

If f(x) is the primitive of $\frac{\sin\sqrt[3]{x}\log(1 + 3x)}{(\tan^{- 1}\sqrt{x})^{2}(e^{\sqrt[3]{x}} - 1)}$ (x ¹ 0), then $\lim_{x \rightarrow 0}f'(x)$ is-

• A. 0
• B. 3/5
• C. 5/3
• D. None

Answer 1

Answer: (B)

3/5

Answer 2

f(x) = $\int \frac { \sin x ^ { 1 / 3 } \log ( 1 + 3 x ) d x } { \left( \tan ^ { - 1 } \sqrt { x } \right) ^ { 2 } \left( e ^ { 5 x ^ { 1 / 3 } } - 1 \right) }$ $\lim _ { x \rightarrow 0 } f ^ { \prime } ( x )$

= $\lim _ { x \rightarrow 0 }$

= $\lim _ { x \rightarrow 0 }$ = $\frac { 1.1 .3 } { 1.1 .5 } =$ 3/5