AP EAMCET · Maths · Continuity and Differentiability
If a real valued function \(f(x)=\left\{\begin{array}{cc}(1+\sin x)^{\operatorname{cosec} x}, & -\pi / 2 < x < 0 \\ a, & x=0 \\ \frac{e^{2 / x}+e^{3 / x}}{a e^{2 / x}+b e^{3 / x}}, & 0 < x < \pi / 2\end{array}\right.\), is continuous at \(\mathrm{x}=0\), then \(\mathrm{ab}=\)
- A e
- B \(\mathrm{e}^2\)
- C 1
- D \(-1\)
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
\(f(0)=a\) \(\lim_{x \to 0^-} (1 + \sin x)^{\operatorname{cosec} x} = e^{\lim_{x \to 0^-} \frac{1}{\sin x}(\sin x)} = e^1 = e\) \(a=e\)…
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