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Questions › IIT JAM › IIT JAM 2023 › Q34
2 marksMathematics › Multivariable calculus › Partial derivatives and differentiabilityHardabout 3 min

IIT JAM 2023 Question 34: Multivariable calculus

Let f(x,y)=x2−y3x2+y2f(x,y)=\dfrac{x^2-y^3}{x^2+y^2}f(x,y)=x2+y2x2−y3​ for (x,y)≠(0,0)(x,y)\ne(0,0)(x,y)=(0,0) and f(0,0)=0f(0,0)=0f(0,0)=0. Then

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Answer and worked solution

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Plain-text version

Let f(x,y)=(x²-y³)/(x²+y²) for (x,y)≠(0,0) and f(0,0)=0. Then (A) f is not continuous at (0,0) (B) fₓ(0,0)=0 (C) f_y(0,0)=-1 (D) fₓ(0,0) does not exist

Also written as: Let f(x,y)=(x^2-y^3)/(x^2+y^2) for (x,y)!=(0,0) and f(0,0)=0. Then

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.

  • IIT JAM 2022 · Q19Let f:ℝ²→ℝ be f(x,y) = (x y²)/(x³ + 2x² y + y³) with f(0,0)=0. Then
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Question from the IIT JAM 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.