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Questions › DSE › DSE 2020 › Q43
4 marks, −1Mathematics › Limits, continuity and differentiability › Continuity and discontinuitiesModerateabout 3 min

DSE 2020 Question 43: Limits, continuity and differentiability

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

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Let ⌊ x⌋ be the greatest integer ≤ x and ⌈ x⌉ the smallest 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 and ceil(x) the smallest integer >= x. The function f:R->R defined by f(x)=ceil(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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Practise Limits, continuity and differentiabilityMore on Continuity and discontinuities

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Question from the DSE 2020 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.