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Questions › UoH › UoH 2021 › Q81
1 mark, −0.33Mathematics › Multivariable calculus › Homogeneous functions and Euler's theoremHardabout 2 min

UoH 2021 Question 81: Multivariable calculus

Given the function W(x1,x2)=log⁡(x12−x22)−log⁡(x12+x22)W(x_1, x_2) = \log(x_1^2 - x_2^2) - \log(x_1^2 + x_2^2)W(x1​,x2​)=log(x12​−x22​)−log(x12​+x22​), the value of the function, Y=x1W1+x2W2Y = x_1 W_1 + x_2 W_2Y=x1​W1​+x2​W2​ (where W1W_1W1​ and W2W_2W2​ are first order partial derivatives w.r.t. x1x_1x1​ and x2x_2x2​ respectively), is:

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Given the function W(x₁, x₂) = log (x₁² - x₂²) - log (x₁² + x₂²), the value of the function, Y = x₁ W₁ + x₂ W₂ (where W₁ and W₂ are first order partial derivatives w.r.t. x₁ and x₂ respectively), is: (A) Zero (B) 25 (C) +1 or -1 (D) can not be determined

Also written as: Given the function W(x_1, x_2) = log (x_1^2 - x_2^2) - log (x_1^2 + x_2^2), the value of the function, Y = x_1 W_1 + x_2 W_2 (where W_1 and W_2 are first order partial derivatives w.r.t. x_1 and x_2 respectively), 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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