Question
Question: The value of \(\lim_{x \rightarrow 0}\left( \frac{\int_{0}^{x^{2}}{\sec^{2}tdt}}{x\sin x} \right)\) ...
The value of limx→0(xsinx∫0x2sec2tdt) is
A
3
B
2
C
1
D
0
Answer
1
Explanation
Solution
limx→0dxd(xsinx)dxd∫0x2sec2tdt=limx→0sinx+xcosxsec2x2.2x
(By L' –Hospital's rule)
= limx→0(xsinx+cosx)2sec2x2=1+12×1=1.