AP EAMCET · Maths · Limits
If \(\lim _{x \rightarrow 0}\left\{1+x \log \left(1+a^2\right)\right\}^{1 / x}=2 a \sin ^2 \theta, a>0\) and \(\theta \in R\), then
- A \(\theta=n \pi \pm \frac{\pi}{2},(n \in Z)\)
- B \(\theta=2 n \pi \pm \frac{\pi}{2},(n \in Z)\)
- C \(\theta=n \pi+\frac{\pi}{2},(n \in Z)\)
- D \(\theta=n \pi \pm \frac{\pi}{4},(n \in Z)\)
Answer & Solution
Correct Answer
(A) \(\theta=n \pi \pm \frac{\pi}{2},(n \in Z)\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0}\left\{1+x \log \left(1+a^2\right)\right\}^{1 / x}\) \[ =2 a \sin ^2 \theta, a>0 \text { and } \theta \in R \] LHS \(\lim _{x \rightarrow 0}\left\{1+x \log \left(1+a^2\right)\right\}^{1 / x}\) is of the form \(\infty 1^{\infty}\)…
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