WBJEE · Maths · Limits
The value of \(\lim _{x \rightarrow 0} \frac{\int_{0}^{x^{2}} \cos \left(t^{2}\right) d t}{x \sin x}\) is
- A 1
- B -1
- C 2
- D \(\log _{e} 2\)
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0} \frac{\int_{0}^{x^{2}} \cos \left(t^{2}\right) d t}{x \sin x} \quad\left[\frac{0}{0}\text{ form}\right]\) \(=\lim _{x \rightarrow 0} \frac{\cos \left(x^{4}\right) \times 2 x}{\sin x+x \cos x} \quad\) [L' Hospital's rule]…
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