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Questions › IIT JAM › IIT JAM 2024 › Q38
2 marksMathematics › Multivariable calculus › Partial derivatives and differentiabilityHardabout 3 min

IIT JAM 2024 Question 38: Multivariable calculus

Let f:R2→Rf: R^2 \to Rf:R2→R be f(x,y)=x2yx4+y2f(x,y) = \dfrac{x^2 y}{x^4 + y^2}f(x,y)=x4+y2x2y​ if (x,y)≠(0,0)(x,y) \neq (0,0)(x,y)=(0,0), and f(0,0)=0f(0,0)=0f(0,0)=0. Which of the following is/are CORRECT?

Select all that apply.

Answer and worked solution

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Plain-text version

Let f: R² → R be f(x,y) = (x² y)/(x⁴ + y²) if (x,y) ≠ (0,0), and f(0,0)=0. Which of the following is/are CORRECT? (A) lim_((x,y)→(0,0)) f(x,y) = 0 (B) fₓ(0,0) = 0 (C) f(x,y) is not continuous at (0,0) (D) Both fₓ and f_y do not exist at (0,0)

Also written as: Let f: R^2 -> R be f(x,y) = (x^2 y)/(x^4 + y^2) if (x,y) != (0,0), and f(0,0)=0. Which of the following is/are 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.

  • 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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