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Compute the linear approximation?

Compute the linear approximation of f(x, y)=sqrt(x^2+y^2) at (3, 0).

Answer: L(x, y)=x

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1 Answer

f(x, y) = 3 at  (3,0)

fx  =   x/(x^2 + y^2)^(1/2) =  1 at (3, 0)           

fy  =  y/(x^2 + y^2)^(1/2)  =  0

L (x,y)  =  L(3, 0) = 3  +  1(x - 3)  +  0(y - 0)

           =                3  +   x   -3

           =                x