WBJEE · Maths · Limits
The value of the limit \(\lim _{x \rightarrow 1} \frac{\sin \left(e^{x-1}-1\right)}{\log x}\) is
- A 0
- B \(e\)
- C \(\frac{1}{e}\)
- D 1
Answer & Solution
Correct Answer
(D) 1
Step-by-step Solution
Detailed explanation
\text { Hints } \begin{aligned} &: \operatorname{Lt}_{h \rightarrow 0} \frac{\sin \left(e^h-1\right)}{\log (1+h)} \quad \text { Put } x=1+h \\ &=\operatorname{Lt}_{h \rightarrow 0} \frac{\sin \left(e^h-1\right)}{\left(e^h-1\right)} \cdot \frac{\left(e^h-1\right)}{\log (1+h)} \\…
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