By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 2 2024 Maths, question 74

Topic: Differential calculus

Q74

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

  1. (a) Limit exists and is equal to 11
  2. (b) Limit exists and is equal to 00
  3. (c) Limit exists and is equal to −1-1
  4. (d) Limit does not existCorrect answer

Solution.

Answer: (d) Limit does not exist

  1. For x>3 the quotient is 1, while for x<3 it is −1.
  2. The right- and left-hand limits differ, so the two-sided limit does not exist.