TS EAMCET · Maths · Continuity and Differentiability
If the real valued function \(f(x)=\left\{\begin{array}{cc}\frac{\left(4^x-1\right)^4 \cot (x \log 4)}{\sin (x \log 4) \log \left(1+x^2 \log 4\right)}, & \text { if } x \neq 0 \ k, & \text { if } x=0\end{array}\right.\) is continuous at \(x=0\), then \(e^k=\)
- A \(1\)
- B \(4\)
- C \(e\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(4\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0} \frac{\left(4^x-1\right)^4 \cot (x \log 4)}{\sin (x \log 4) \log \left(1+x^2 \log 4\right)} \\ & =\lim _{x \rightarrow 0} \frac{\left(4^x-1\right)^4 \cos (x \log 4)}{\sin ^2(x \log 4) \log…
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