If , what is the value of

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Question

This question was previously asked in

UPSC ESE 2018 Paper 1

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Answer 1

Concept:

A function f(x, y) is said to be homogeneous of degree n in x and y, it can be written in the form

f(λx, λy) = λn f(x, y)

Euler’s theorem:

If f(x, y) is a homogeneous function of degree n in x and y and has continuous first and second-order partial derivatives, then

If z is homogeneous function of x & y of degree n and z = f(u), then

Calculation:

Given,

z is a homogenous function of x & y with a degree 1.

Now, z = eu

Thus, by Euler’s theorem: