Engineering Calculus Notes 303

Engineering Calculus Notes 303 - + y 2 ( x,y ) 2 = 1 and (1...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
3.5. SURFACES AND THEIR TANGENT PLANES 291 at the point (1 , 1 , 2), these values are ∂f ∂x (1 , 1 , 2) = 8 ∂f ∂y (1 , 1 , 2) = 2 ∂f ∂z (1 , 1 , 2) = 4 so we see from the Implicit Function Theorem that we can solve for any one of the variables in terms of the other two. For example, near this point we can write z = φ ( x,y ) where 4 x 2
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: + y 2 ( x,y ) 2 = 1 and (1 , 1) = 2; the theorem tells us that ( x,y ) is dierentiable at x = 1, y = 1, with x (1 , 1) = f/x f/z = 8 4 = 2 and y (1 , 1) = f/y f/z = 2 4 = 1 2 ....
View Full Document

Ask a homework question - tutors are online