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Questions › DSE › DSE 2008 › Q59
2 marksMathematics › Limits, continuity and differentiability › Continuity and discontinuitiesModerateabout 3 min

DSE 2008 Question 59: Limits, continuity and differentiability

The function f(x)=sin⁡(1/x)f(x)=\sin(1/x)f(x)=sin(1/x) if x>0x>0x>0 and f(x)=af(x)=af(x)=a if x=0x=0x=0 (with fff defined for x≥0x\ge 0x≥0)

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Plain-text version

The function f(x)=sin (1/x) if x>0 and f(x)=a if x=0 (with f defined for x≥ 0) (A) is continuous or discontinuous at x=0, depending on the value a (B) is continuous at x=0 (C) is discontinuous at x=0 (D) is upper hemicontinuous at x=0

Also written as: The function f(x)=sin (1/x) if x>0 and f(x)=a if x=0 (with f defined for x>= 0)

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 2008 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.