Question
State Euler’s theorem for homogeneous functions and verify it for the function:
Answer :
Word Count : 327
Euler's Theorem for homogeneous functions states that if \( f(x, y) \) is a homogeneous function of degree \( n \), then: \[ x \frac{\partial f}{\partial x} + y \frac{\partial f}{\partial y} = n f(x, y) \] Now, let's verify this theorem for the function \( u = \frac{x^3 + y^3}{x + y} \). ### Step 1: Find the partial derivatives of \( u \). _________ _____ __________ ____ ____ __________.
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Euler's Theorem for homogeneous functions states that if \( f(x, y) \) is a homogeneous function of degree \( n \), then: \[ x \frac{\partial f}{\partial x} + y \frac{\partial f}{\partial y} = n f(x, y) \] Now, let's verify this theorem for the function \( u = \frac{x^3 + y^3}{x + y} \). ### Step 1: Find the partial derivatives of \( u \). _________ _____ __________ ____ ____ __________.
__________ _______ ___ ___ __________ _____ ________ ____ ____ _________ _______.
_____ ________ _________ ___ ___ ____ _________.
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Related Questions
युगपत समीकरणों :
का हल प्राप्त कीजिए।
दिखाइए कि निम्नलिखित फलन f, (0,0) पर अवकलनीय है :
Show that the following function is not continuous at (0,0):
हल कीजिए :
y'=zy$+x 4 / xy3
Solve the differential equations:
Using Charpit’s method, find the complete integral of the differential equation:
p2x + q2y = z
If:
Z= x²y+2xy²
where x = sin zt
and
y = cost
find dz/dt when t=0by (i) chain rule and by (ii) the direct substitution.
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