Q94 / 160 · AP EAMCET 2015 · Mathematics

If $g(x)=\frac{x}{[x]}$ for $\mathrm{x}>2$, then $\lim _{x \rightarrow 2} \frac{g(x)-g(2)}{x-2}$ is equal to

  • A
    $-1$
  • B
    $0$
  • Correct answer
    C
    $\frac{1}{2}$
  • D
    $2$

Solution

Given, $g(x)=\frac{x}{[x]}$ When, $x>2$, then $[x]=2 \Rightarrow g(x)=\frac{x}{2}$ Now, $\quad \lim _{x \rightarrow 2} \frac{g(x)-g(2)}{x-2}=\lim _{x \rightarrow 2} \frac{\frac{x}{2}-1}{x-2}$ $=\lim _{x \rightarrow 2} \frac{x-2}{2(x-2)}=\lim _{x \rightarrow 2}\left(\frac{1}{2}\right)=\frac{1}{2}$

Hence, the correct answer is option: 'C'.

Relevant Questions