Q249 / 270 · NDA 2023 (Phase 1) · Mathematics

What is $\lim _{x \rightarrow 5} \frac{5-x}{|x-5|}$ equal to?

  • A
    $-1$
  • B
    $0$
  • C
    $1$
  • Correct answer
    D
    Limit does not exist

Solution

$\lim _{x \rightarrow 5} \frac{5-x}{|x-5|}$ LHL: $\lim _{x \rightarrow 5^{-}} \frac{5-x}{-(x-5)}=\lim _{x \rightarrow 5^{-}} \frac{5-x}{5-x}=1$ RHL: $\lim _{x \rightarrow 5^{+}} \frac{5-x}{(x-5)}=\lim _{x \rightarrow 5^{+}}(-1)=-1$ $\therefore \quad$ LHL $\neq$ RHL $\therefore$ Limit does not exist.

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

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