AP EAMCET · Maths · Continuity and Differentiability
Let \(f(x)= \begin{cases}\frac{5 e^{1 / x}+2}{3-e^{1 / x}}, & x \neq 0 \\ 0, & x=0\end{cases}\) Then at \(x=0, x f(x)\) and \(f(x)\) are respectively
- A Differentiable and continuous
- B Continuous and differentiable
- C Continuous and not differentiable
- D Not differentiable and continuous
Answer & Solution
Correct Answer
(C) Continuous and not differentiable
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{cc}\frac{5 e^{1 / x}+2}{3-e^{1 / x}} & x \neq 0 \\ 0 & x=0\end{array}\right.\) Then \(x f(x)=\left\{\begin{array}{cc}\frac{x\left(5 e^{1 / x}+2\right)}{3-e^{1 / x}} & x \neq 0 \\ 0 & x=0\end{array}\right.\) Let us check continuity of \(x f(x)\) at…
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