if then, lim x → 0 + f ( x ) = e, lim x → 0 − f ( x ) = e 2, f ( x ) is discontinuous at x = 0, None of these

lim x → 0 − f ( x ) = lim x → 0 [ ( 1 + 2 x ) 1/2 x ] 2 = e 2 .

if then

Question: Answered & Verified by Expert

then

MathematicsContinuity and DifferentiabilityJEE Main

Options:

Solution:

1308 Upvotes Verified Answer

The correct answer is: $\lim _{x \rightarrow 0^-} f(x)=e^2$

$\lim _{x \rightarrow 0^-} f(x)=\lim _{x \rightarrow 0}\left[(1+2 x)^{1 / 2 x}\right]^2=e^2$.

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