Question

$f(x)=\frac{|x-a|}{x-a}$ , when $x\neq a=1$ , when $x = a$ then

• A. $f$ is continuous everywhere
• B. $f$ is continuous at $x = a$.
• C. $f$ has a limit 1 at $x = a$
• D. limit of $f$ does not exist at $x = a$.

Answer 1

Answer: (D)

limit of $f$ does not exist at $x = a$.

Answer 2

$\lim_{x\to a-} f\left(x\right) = - 1 ,\lim_{x\to a+} f\left(x\right) = 1$ $\therefore$ $\lim_{x\to a} f\left(x\right)$ does not exist.