If f (x) = {cases} {x(3e¹/x}+4)}{2-e¹/x}} & x ≠ 0 \\ 0 & x = 0 {cases}, then f (x) is

Correct Answer is : Continuous but not differentiable at x = 0

Continuous aswell as differentiable at x = 0

Continuous but not differentiable at x = 0

Differentiable but not Continuous at x = 0

Correct Answer is : Continuous but not differentiable at x = 0

Test Index

JEE Mains 2020 Model Paper 1 New Pattern

Question : 4 of 75

Marks: +1, -0

If f (x) =

\begin{cases} \frac{x(3e^{1/x}+4)}{2-e^{1/x}} & x \neq 0 \\ 0 & x = 0 \end{cases}

, then f (x) is

Solution:

f' (0) =

\lim\limits_{h\to 0} \frac{f(0-h)-f(0)}{-h}

\lim\limits_{h\to 0}\left(\frac{-h(3e^{-1/h}+4)}{2-e^{-1/h}}-0\right)\left(\frac{-1}{h}\right)

= 2

Rf^1(0)

\lim\limits_{h\to 0} \frac{f(0+h)-f(0)}{h}

\lim\limits_{h\to 0}\left(\frac{h\left(3e^{1/h}+4\right)}{2-e^{1/h}}-0\right)\left(\frac{1}{h}\right)

\lim\limits_{h\to 0}\left(\frac{3+4e^{-1/h}}{2e^{-1/h}-1}\right)

= - 3

Since

Lf^1

(0) ≠

Rf^1

(0)

∴ f (x) is differentiable at x=0. But f (x) is continuous at x = 0

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