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 2012 › Q49
2 marksMathematics › Limits, continuity and differentiability › Differentiability and its link to continuityModerateabout 3 min

DSE 2012 Question 49: Limits, continuity and differentiability

The real valued function f(x)=x+∣x∣+(x−1)+∣x−1∣f(x)=x+|x|+(x-1)+|x-1|f(x)=x+∣x∣+(x−1)+∣x−1∣, where ∣x∣,∣x−1∣|x|,|x-1|∣x∣,∣x−1∣ stand for absolute values

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

The real valued function f(x)=x+|x|+(x-1)+|x-1|, where |x|,|x-1| stand for absolute values (A) Is differentiable everywhere except at x=0 (B) Is not continuous at 0 (C) Is not differentiable at 1 (D) Is not continuous at 1

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 2012 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.