Skip to content
We use only essential cookies to keep you signed in and remember your preferences. See our Cookie Policy.
TestStop
MocksPracticeResourcesIndiaBlogPricing
Sign in
Questions › DSE › DSE 2009 › Q25
2 marksMathematics › Limits, continuity and differentiability › Differentiability and its link to continuityHardabout 4 min

DSE 2009 Question 25: Limits, continuity and differentiability

Consider the function f(x)=x2sin⁡(1/x)f(x)=x^{2}\sin(1/x)f(x)=x2sin(1/x) for x≠0x\ne 0x=0 and f(0)=0f(0)=0f(0)=0. Then the following is true about the derivative of fff:

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

Consider the function f(x)=x²sin (1/x) for x≠ 0 and f(0)=0. Then the following is true about the derivative of f: (A) f′(0)=-1 and f′(x) is continuous at x=0. (B) f′(0)=-1 and f′(x) is discontinuous at x=0. (C) f′(0)=0 and f′(x) is discontinuous at x=0. (D) f′(x) is not defined at x=0.

Also written as: Consider the function f(x)=x^2sin (1/x) for x!= 0 and f(0)=0. Then the following is true about the derivative of f:

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
Practise Limits, continuity and differentiabilityMore on Differentiability and its link to continuity

Similar questions from other papers

  • CUET-PG 2026 · Q24Derivative of Average cost (AC) = 5 + 2/Q is
  • IIT JAM 2026 · Q50The value of the first derivative of f(x)=(3x³+2x²+x+1)² evaluated at x=2 is (*in integer*).
  • UGC-NET 2026 · Q8What will be the third derivative of the following rational function? y = g(x) = x/(1+x); (x ≠ -1)
  • CUET-PG 2025 · Q3The exports of goods of a country, G = G(t) has a growth rate of a/t, and its exports of services, S = S(t) has a growth rate of b/t. What is the growth rate of its…
  • GATE 2025 · Q32Let f(x) = -3x²(1-x) - 3x(1-x)² - (1-x)³. Then, df(x)/dx =

Question from the DSE 2009 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.