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Questions › DSE › DSE 2020 › Q41
4 marks, −1Mathematics › Limits, continuity and differentiability › Continuity and discontinuitiesModerateabout 3 min

DSE 2020 Question 41: Limits, continuity and differentiability

Let ⌊x⌋\lfloor x\rfloor⌊x⌋ be the greatest integer ≤x\le x≤x. The function f:R→Rf:\mathbb{R}\to\mathbb{R}f:R→R defined by f(x)=x−⌊x⌋f(x)=x-\lfloor x\rfloorf(x)=x−⌊x⌋ is

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Let ⌊ x⌋ be the greatest integer ≤ x. The function f:ℝ→ℝ defined by f(x)=x-⌊ x⌋ is (A) Left-discontinuous at an integer (B) Right-discontinuous at an integer (C) Left-discontinuous and right-discontinuous at an integer (D) Discontinuous everywhere

Also written as: Let floor(x) be the greatest integer <= x. The function f:R->R defined by f(x)=x-floor(x) is

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

What this question tests

This question is on Continuity and discontinuities, part of Limits, continuity and differentiability in Mathematics.

When a function is continuous at a point and what kinds of breaks occur.

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