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AP EAMCET · Maths · Limits

If \(A \neq 0\) and \(x>0\), then \(\lim _{n \rightarrow \infty} \frac{\cos x-e^{n x}}{1-A e^{n x}}=\)

  1. A Does not exist
  2. B \(1\)
  3. C \(\frac{\cos x}{A}\)
  4. D \(\frac{1}{A}\)
Verified Solution

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] \\ &…