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Limits Continuity and Differentiability question

2021 · 18 Mar · Shift 2 · Q42

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JEE Main
Mathematics
Limits Continuity and Differentiability
2021 · 18 Mar · Shift 2 · Q42

Limits Continuity and Differentiability question

2021 · 18 Mar · Shift 2 · Q42

JEE MainMathematicsLimits Continuity and DifferentiabilityNumerical+4 / −1

Let f : R

\to

R satisfy the equation f(x + y) = f(x) . f(y) for all x, y

\in

R and f(x)

e

0 for any x

\in

R. If the function f is differentiable at x = 0 and f'(0) = 3, then

\mathop {\lim }\limits_{h \to 0} {1 \over h}(f(h) - 1)

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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