Question

Let $f\left(x\right)$ is a function, defined as $f\left(x\right)=\begin{cases} 3x^{2}+2x+5;x>0 \\ 4;x=0 \\ x^{2}-4x+3;x < 0 \end{cases}$ then $\displaystyle\lim _{x \rightarrow 0^{+}} f(\{x-\sin x\})$ equals $[$ Note: $\{\cdot\}$ denotes fractional part function.]

• A. $3$
• B. $4$
• C. $5$
• D. None

Answer 1

Answer: (C)

If $x=0+h$
$\therefore \left\{\right.x-sinx\left.\right\}=\left\{\right.h-sinh\left.\right\}$
$=\left(\right.h-sinh\left.\right)-\left[\right.h-sinh\left]\right.=h-sinh$
$\therefore f\left(\right.h-sinh\left.\right)=5$