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NDA 2019 Maths · Mathematics · Continuity and Differentiability · medium

Every function that is continuous on a closed interval [a,b] is bounded on [a,b]. 2. If lim x→ af(x) exists, then f is continuous at x=a.

Single correct option

Consider the following statements:
1. Every function that is continuous on a closed interval [a,b][a,b] is bounded on [a,b][a,b].
2. If lim⁡x→af(x)\lim_{x\to a}f(x) exists, then ff is continuous at x=ax=a.
Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (A) 1 only

Statement 1 is the boundedness theorem for continuous functions on a closed interval; true. Statement 2 is false: continuity at aa also requires f(a)f(a) to be defined and equal to the limit. For f(x)=x2−1x−1f(x)=\frac{x^2-1}{x-1} the limit at 11 exists and equals 22, but f(1)f(1) is undefined. Only statement 1 is correct.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake