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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Limits

NDA 2024 · Mathematics · Limits

Which one of the following is correct regarding _ x arrow 3...

Which one of the following is correct regarding lim⁡x→3∣x−3∣x−3?\lim _{x \rightarrow 3} \frac{|x-3|}{x-3} ?

Options

  1. ALimits exists and is equal to 1
  2. BLimits exists and is equal to 0
  3. CLimits exists and is equal to -1
  4. DLimit does not exist

Correct answer

D. Limit does not exist

Step-by-step solution

Given, lim⁡x→3∣x−3∣x−3\lim _{x \rightarrow 3} \frac{|x-3|}{x-3} Finding LRL and RHL at x=3LHL=lt⁡x→3−∣x−3∣x−3=−(x−3)x−3=−1LHL=lt⁡x→3+∣x−3∣x−3=(x−3)x−3=+1x=3\mathrm{LHL}=\operatorname{lt}_{\mathrm{x} \rightarrow 3^{-}} \frac{|\mathrm{x}-3|}{\mathrm{x}-3}=\frac{-(\mathrm{x}-3)}{\mathrm{x}-3}=-1\mathrm{LHL}=\operatorname{lt}_{\mathrm{x} \rightarrow 3^{+}} \frac{|\mathrm{x}-3|}{\mathrm{x}-3}=\frac{(\mathrm{x}-3)}{\mathrm{x}-3}=+1 LHL ≠ RHL, limit does not exist.
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