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Questions › IIT JAM › IIT JAM 2023 › Q5
1 mark, −0.333Mathematics › Multivariable calculus › Implicit functions, level curves and second-order conditionsVery Hardabout 4 min

IIT JAM 2023 Question 5: Multivariable calculus

Which statement is CORRECT? S1: x2+y2=6x^2+y^2=6x2+y2=6 is a level curve of f(x,y)=x2+y2−x2−y2+2f(x,y)=\sqrt{x^2+y^2}-x^2-y^2+2f(x,y)=x2+y2​−x2−y2+2. S2: x2−y2=−3x^2-y^2=-3x2−y2=−3 is a level curve of g(x,y)=e−x2ey2+x4−2−2x2y2+y4g(x,y)=e^{-x^2}e^{y^2}+x^4-2-2x^2y^2+y^4g(x,y)=e−x2ey2+x4−2−2x2y2+y4.

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Which statement is CORRECT? S1: x²+y²=6 is a level curve of f(x,y)=√(x²+y²)-x²-y²+2. S2: x²-y²=-3 is a level curve of g(x,y)=e^(-x²)e^(y²)+x⁴-2-2x²y²+y⁴. (A) both S1 and S2 (B) only S1 (C) only S2 (D) neither S1 nor S2

Also written as: Which statement is CORRECT? S1: x^2+y^2=6 is a level curve of f(x,y)=sqrt(x^2+y^2)-x^2-y^2+2. S2: x^2-y^2=-3 is a level curve of g(x,y)=e^(-x^2)e^(y^2)+x^4-2-2x^2y^2+y^4.

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

What this question tests

This question is on Implicit functions, level curves and second-order conditions, part of Multivariable calculus in Mathematics.

Slopes of level curves and implicit functions, and conditions for optima in two variables.

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