JEE Advanced · MathematicsEasy

$lim_{x \to 0} \frac{e ^{x} - 1}{x}$

A. $0$
B. $e$
C. $1$
D. $Does not exist$

Show correct answer & step-by-step solution

Correct answer: C — $1$

Solution

By the definition of the derivative of f (x) = e^{x} at x = 0, x \to 0 lim \frac{e ^{x} - e ^{0}}{x - 0} = f^{'} (0) = e^{0} = 1 .

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Evaluate the limit of (e to the power of x minus 1) divided by x as x approaches… — JEE Advanced Mathematics Question with Solutio