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Questions › DSE › DSE 2015 › Q7
1 mark, −0.333333333333333Mathematics › Multivariable calculus › Partial derivatives and differentiabilityModerateabout 3 min

DSE 2015 Question 7: Multivariable calculus

For the same fff (f(0,0)=0f(0,0)=0f(0,0)=0, f(x,y)=xyx2+y2f(x,y)=\dfrac{xy}{x^2+y^2}f(x,y)=x2+y2xy​ otherwise), which statement is correct?

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Plain-text version

For the same f (f(0,0)=0, f(x,y)=xy/(x²+y²) otherwise), which statement is correct? (A) f is continuous and differentiable (B) f is discontinuous and differentiable (C) f is continuous but not differentiable (D) f is discontinuous and non-differentiable

Also written as: For the same f (f(0,0)=0, f(x,y)=xy/(x^2+y^2) otherwise), which statement is correct?

Multivariable calculus has come up 32 times in 7 exams since 2007.

What this question tests

This question is on Partial derivatives and differentiability, part of Multivariable calculus in Mathematics.

Derivatives with respect to one variable at a time, and how they relate to continuity and differentiability.

TestStop has 12 past-paper questions on this subtopic; the nearest in year are below.

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Question from the DSE 2015 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.