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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Limits

NDA 2023 · Mathematics · Limits

What is _ x arrow 5 (5-x)/(|x-5|) equal to?

What is lim⁡x→55−x∣x−5∣\lim _{x \rightarrow 5} \frac{5-x}{|x-5|} equal to?

Options

  1. A−1-1
  2. B00
  3. C11
  4. DLimit does not exist

Correct answer

D. Limit does not exist

Step-by-step solution

lim⁡x→55−x∣x−5∣\lim _{x \rightarrow 5} \frac{5-x}{|x-5|} LHL: lim⁡x→5−5−x−(x−5)=lim⁡x→5−5−x5−x=1\lim _{x \rightarrow 5^{-}} \frac{5-x}{-(x-5)}=\lim _{x \rightarrow 5^{-}} \frac{5-x}{5-x}=1 RHL: lim⁡x→5+5−x(x−5)=lim⁡x→5+(−1)=−1∴\lim _{x \rightarrow 5^{+}} \frac{5-x}{(x-5)}=\lim _{x \rightarrow 5^{+}}(-1)=-1\therefore \quad LHL ≠ RHL ∴\therefore Limit does not exist.
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