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Questions › DSE › DSE 2020 › Q31
4 marks, −1Mathematics › Multivariable calculus › Homogeneous functions and Euler's theoremModerateabout 3 min

DSE 2020 Question 31: Multivariable calculus

Given a non-empty set C⊆RnC\subseteq\mathbb{R}^nC⊆Rn, for every p∈R+np\in\mathbb{R}^n_+p∈R+n​ let c(p)∈Cc(p)\in Cc(p)∈C satisfy p⋅c(p)≤p⋅cp\cdot c(p)\le p\cdot cp⋅c(p)≤p⋅c for every c∈Cc\in Cc∈C. Then the function e(p)=p⋅c(p)e(p)=p\cdot c(p)e(p)=p⋅c(p) is

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Given a non-empty set C⊆ℝⁿ, for every p∈ℝⁿ₊ let c(p)∈ C satisfy p· c(p)≤ p· c for every c∈ C. Then the function e(p)=p· c(p) is (A) homogeneous of degree 0 (B) homogeneous of degree 1 (C) homogeneous of degree ∞ (D) non-homogeneous

Also written as: Given a non-empty set C subseteq R^n, for every p in R^n_+ let c(p) in C satisfy p* c(p)<= p* c for every c in C. Then the function e(p)=p* c(p) is

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

What this question tests

This question is on Homogeneous functions and Euler's theorem, part of Multivariable calculus in Mathematics.

Functions that scale in a fixed way when all inputs scale, and the identity this gives.

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

  • IIT JAM 2022 · Q38Which of the following functions is/are homogeneous?
Practise Multivariable calculusMore on Homogeneous functions and Euler's theorem

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Question from the DSE 2020 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.