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