MCQ
If $f (x)=|x-2|$, then
  • A
    $\lim _{x \rightarrow z^{+}} f(x) \neq 0$
  • B
    $\lim _{x \rightarrow 2^{-}} f (x) \neq 0$
  • C
    $\lim _{x \rightarrow 2^{+}} f(x) \neq \lim _{x \rightarrow 2^{-}} f(x)$
  • $f (x)$ is continuous at $x=2$

Answer

Correct option: D.
$f (x)$ is continuous at $x=2$
(D)
Here, f(2) = 0
$\lim _{x \rightarrow 2^{-}} f (x)=\lim _{ h \rightarrow 0} f (2- h )=\lim _{ h \rightarrow 0}|2- h -2|=0$
$\lim _{x \rightarrow 2^{+}} f(x)=\lim _{h \rightarrow 0} f(2+h)=\lim _{h \rightarrow 0}|2+h-2|=0$
$\therefore \quad f (x)$ is continuous at $x=2$.

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