Compute the linear approximation of f(x, y)=sqrt(x^2+y^2) at (3, 0).
Answer: L(x, y)=x
Compute the linear approximation of f(x, y)=sqrt(x^2+y^2) at (3, 0).
Answer: L(x, y)=x
f(x, y) = 3 at (3,0)
f_{x} = x/(x^2 + y^2)^(1/2) = 1 at (3, 0)
f_{y} = 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