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) = π2 , and f"'(0) = π9
and
g(0) = ln 2, g'(0) = π, g′′(0) = π2, and g'"(0) = π3.
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)

Answer 1

The correct answer is : 2.