If f ( x )= array cc x (3 e ^ 1 / x +4 ) 2- e ^ 1 / x ; & x 0 0 ; & x =0 array . then
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
If \[\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc}
\frac{\mathrm{x}\left(3 \mathrm{e}^{1 / \mathrm{x}}+4\right)}{2-\mathrm{e}^{1 / \mathrm{x}}} ; & \mathrm{x} \neq 0 \\
0 ; & \mathrm{x}=0
\end{array}\right.\] then
- \(\lim _{x \rightarrow 0} f(x)=1\)
- f (x) is continuous at x = 0
- f (x) is differentiable at x = 0
- None of these
Answer
(B) f (x) is continuous at x = 0
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