AP EAMCET · Maths · Continuity and Differentiability
If a function defined by \(f(x)=\frac{\left(3^x-1\right)^2}{\sin x \log (1+x)}, x \neq 0\), is continuous at \(\mathrm{x}=0\), then \(\mathrm{f}(0)=\)
- A \(2 \log 3\)
- B \(\log 3^2\)
- C \(2+\log 3\)
- D \((\log 3)^2\)
Answer & Solution
Correct Answer
(B) \(\log 3^2\)
Step-by-step Solution
Detailed explanation
Given \(f(x)=\frac{\left(3^x-1\right)^2}{\sin x \log (1+x)}, x \neq 0\) Now, \(\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0} \frac{\left(3^x-1\right)^2}{\sin x \log (1+x)}\)…
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