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Questions › JNU › JNU SSS 2016 › Q31
1 markMathematics › Limits, continuity and differentiability › Differentiability and its link to continuityEasyabout 1 min

JNU SSS 2016 Question 31: Limits, continuity and differentiability

Let f(x)f(x)f(x) be differentiable for all xxx such that 0<x<10 < x < 10<x<1. Which of the following statements is true?

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Let f(x) be differentiable for all x such that 0 < x < 1. Which of the following statements is true? (A) f(x) is continuous for all x such that 0 < x < 1 (B) f(x) is continuous when x < 1/2 but discontinuous at some other x (C) We cannot say anything about the truth of (a) and (b) given the information (D) None of the above

Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.

What this question tests

This question is on Differentiability and its link to continuity, part of Limits, continuity and differentiability in Mathematics.

When a derivative exists and why differentiability implies continuity but not conversely.

TestStop has 12 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2021 · Q35Let f be defined on (-π/2, π/2) by f(x) = (cos (π/2 + |x|))/(sin (π/2 - |x|)). Then,
  • IIT JAM 2022 · Q34Let f be defined by f(x) = |x| + |cos (π/2 - x)| for x ∈ (-π/2, π/2). Then
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Question from the JNU SSS 2016 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.