Let f: R \to R satisfy the equation f(x+y)=f(x) \cdot f(y) for all x, y \in R and f(x) \neq 0 for any x \in R. If the function f is differentiable at x=0 and f^{'}(0)=3, then \lim_{h \to 0} \frac{1}{h}(f(h)-1) is equal to........... [18 Mar 2021 Shift 2]

Limits, Continuity and Differentiability Part 2

Section: Mathematics

Question : 77 of 100

Marks: +1, -0

Let f:R→R satisfy the equation f(x+y)=f(x)⋅f(y) for all x,y∈R and f(x)≠0 for any x∈R. If the function f is differentiable at x=0 and f′(0)=3, then

lim

h→0

‌

(f(h)−1) is equal to...........

[18 Mar 2021 Shift 2]

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