Answer: Homogeneous Functions A function is homogeneous of degree if In Exercises 43 46
Chapter 13, Problem 45(choose chapter or problem)
A function is homogeneous of degree n if \(f(t x, t y)=t^{n} f(x, y)\). In Exercises 43– 46, (a) show that the function is homogeneous and determine and (b) show that \(x f_{x}(x, y)+y f_{y}(x, y)=n f(x, y)\).
\(f(x, y)=e^{x / y}\)
Text Transcription:
f(tx,ty)=t^nf(x,y)
xf_x(x,y)+yf_y(x,y)=nf(x,y)
f(x,y)=e^x/y
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