Limits and Continuity: Exponential limit MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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Exponential limitHardQuestion 240015

Question

lim(x→0) (aˣ − 1)/x equals:

A
ln a
Correct
B
a
C
1/a
D
0

Correct answer

ln a

Explanation

Using the derivative definition: d/dx(aˣ) at x = 0 = aˣ ln a at x = 0 = ln a. Equivalently: aˣ = e^(x ln a) so (aˣ−1)/x = (e^(x ln a)−1)/x → ln a as x → 0.

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