ISI2020-MMA: 18

Question

Let $f : [0, \infty ) \rightarrow \mathbb{R}$ be a differentiable function with $f(0) = 1$ and $f(x) f’ (x) > 0$, for all $x$. Let $\text{A} (n)$ be the area of region bounded by $x$ – axis, $y$ – axis, graph of $f$ and the line $x = n$. Then

• A. $\left \{ \text{A} (n)\right \} _{n \geq 1}$ is a convergent sequence

• B. $\left \{ \text{A} (n)\right \} _{n \geq 1}$ is a oscillatory sequence

• C. The function $\text{A} : \mathbb{N}\rightarrow \mathbb{R}$ is increasing

• D. None of the above statements is true

Answer 1

Answer C.