Question

Let ƒ(x) = $\lim_{x \rightarrow \infty}\left( 1 + \frac{1}{a + bx} \right)^{c + dx}$ (where, [ ] denotes the greatest integer function) and

g (x) = $e^{d/b}$. Then for ƒ(g(x)) at x = 0

• A. $e^{c/a}$ƒ(g(x)) exist but not continuous
• B. Continuous but not differentiable at x = 0
• C. Differentiable at x = 0
• D. $e^{(c + d)/(a + b)}$ƒ(g(x)) does not exist

Answer 1

Answer: (C)

Differentiable at x = 0

Answer 2

Since, ƒ(g(x)) =

Which is always differentiable in $\left[ - \frac { \pi } { 4 } , \infty \right)$ and also

continuous.