Asked by Anonymous
9. Find the linear approximation of the function
f(x,y) = √1+ x^2+ y^2 at the point (x,y,z) = (2, -2, 3).
f(x,y) = √1+ x^2+ y^2 at the point (x,y,z) = (2, -2, 3).
Answers
Answered by
oobleck
assuming you mean
z = f(x,y) = √(1+ x^2+ y^2) then we have the equation of the tangent plane as
z-f(2,-2,3) = ∂f/∂x (x-2) + ∂f/∂y (y+2)
z-3 = 2/√5 (x-2) - 2/√5 (y+2)
z = f(x,y) = √(1+ x^2+ y^2) then we have the equation of the tangent plane as
z-f(2,-2,3) = ∂f/∂x (x-2) + ∂f/∂y (y+2)
z-3 = 2/√5 (x-2) - 2/√5 (y+2)