AP EAMCET · Maths · Limits
If \(A \neq 0\) and \(x>0\), then \(\lim _{n \rightarrow \infty} \frac{\cos x-e^{n x}}{1-A e^{n x}}=\)
- A Does not exist
- B \(1\)
- C \(\frac{\cos x}{A}\)
- D \(\frac{1}{A}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{A}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \lim _{n \rightarrow \infty} \frac{\cos x-e^{n x}}{1-A e^{n x}} \\ & =\lim _{n \rightarrow \infty}\left\{\frac{\left(\frac{\cos x}{e^{n x}}\right)-1}{\left(\frac{1}{e^{n x}}\right)-A}\right\} \quad[-1 \leq \cos x \leq 1, \forall x \in R] \\ &…
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