Let f : (−1, 1) → $\R$ and g : (−1, 1) → $\R$ be thrice continuously differentiable functions such that f(x) ≠ g(x) for every nonzero x ∈ (−1, 1). Suppose f(0) = ln 2, f'(0) = π, f"(0) = π 2 , and f"'(0) = π 9 and g(0) = ln 2, g'(0) = π, g′′(0) = π 2 , and g'"(0) = π 3 . Then the value of the limit $\lim\limits_{x\rightarrow0}\frac{e^{f(x)}-e^{g(x)}}{f(x)-g(x)}$ is equal to _________. (Rounded off to two decimal places)

Question

Let f : (−1, 1) → $\R$  and g : (−1, 1) →  $\R$  be thrice continuously differentiable functions such that f(x) ≠ g(x) for every nonzero x ∈ (−1, 1). Suppose f(0) = ln 2, f'(0) = π, f"(0) = π 2 , and f"'(0) = π 9 and g(0) = ln 2, g'(0) = π, g′′(0) = π 2 , and g'"(0) = π 3 . Then the value of the limit $\lim\limits_{x\rightarrow0}\frac{e^{f(x)}-e^{g(x)}}{f(x)-g(x)}$ is equal to _________. (Rounded off to two decimal places)

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The correct answer is : 2.

Correct Answer: 2

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