KCET · Maths · Continuity and Differentiability
A function is \(f(x)=\left\{\begin{array}{cc}\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}, & \text { if } x \neq 0 \\ 0, & \text { if } x=0\end{array}\right.\)
- A continuous at \(\mathrm{x}=0\)
- B not continuous at \(\mathrm{x}=0\)
- C differentiable at \(\mathrm{x}=0\)
- D differentiable at \(\mathrm{x}=0\), but not continuous at \(\mathrm{x}=0\)
Answer & Solution
Correct Answer
(B) not continuous at \(\mathrm{x}=0\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{cc}
\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1} & , \quad x \neq 0 \\
0 & , x=0
\end{array}\right.\)
LHL \(=-1\), RHL \(=1\), Not continuous.
\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1} & , \quad x \neq 0 \\
0 & , x=0
\end{array}\right.\)
LHL \(=-1\), RHL \(=1\), Not continuous.
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