Question

Let $f\left(x\right)=x+\frac{x}{1+x}+\frac{x}{(1+x{)}^2}+...$ to $\infty$ At $x=0$, $f\left(x\right)$ is

• A. Continuous but not deffernetiable
• B. Differentiable but not continuous
• C. Neither continuous nor differntiable
• D. Continuous as well as differentiable

Answer 1

The correct option is D Continuous as well as differentiable

$f\left(x\right)=x+\frac{x}{1+x}+\frac{x}{{(1+x)}^2}+....\infty$

$f\left(x\right)=\frac{x}{1-\frac{1}{1+x}}=\frac{x}{x}\times (1+x)=1+x$

At $x=0$

$f\left(x\right)$ is continuous as well as differentiable