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Chapter: 12th Maths : UNIT 8 : Differentials and Partial Derivatives

Exercise 8.7: Homogeneous Functions and Euler’s Theorem

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EXERCISE 8.7

1. In each of the following cases, determine whether the following function is homogeneous or not. If it is so, find the degree.



2. Prove that f (xy= x3  2x2y + 3xy2 + y3 is homogeneous; what is the degree? Verify Euler’s Theorem for f .


3. Prove that g(x, y) = x log (y/x) is homogeneous; what is the degree? Verify Euler’s Theorem for g.






Answers:

1. (i) not homogeneous (ii) Homogeneous, deg.3  (iii) homogeneous, deg.0 (iv) not homogeneous

6. 5

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12th Maths : UNIT 8 : Differentials and Partial Derivatives : Exercise 8.7: Homogeneous Functions and Euler’s Theorem | Problem Questions with Answer, Solution

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12th Maths : UNIT 8 : Differentials and Partial Derivatives


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