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Consider the following statements: 1. f(x) = [x], where [.] is the greatest integer function, is discontinuous at x = n, where n ϵ Z. 2. f(x) = cot x is discontinuous at x = nπ, where n ϵ Z.   Which of the above statements is/are correct?

Consider the following statements: 1. f(x) = [x], where [.] is the greatest integer function, is discontinuous at x = n, where n ϵ Z. 2. f(x) = cot x is discontinuous at x = nπ, where n ϵ Z.   Which of the above statements is/are correct? Correct Answer Both 1 and 2

Concept:

  • The greatest integer function is discontinuous at all the integers.
  • For function to be continuous it should be first defined


Calculation:

Statement (1) is correct as the greatest integer function is discontinuous at all the integers.

2. f(x) = cot x

⇒ f(x) = cos x /sin x

At x = nπ, sin x = 0

∴ cot x is not defined at x = nπ

Hence, cot x is discontinuous at x = nπ

So this statement (2) is correct.

Hence, option (3) is correct.

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