{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Engineering Calculus Notes 303

# Engineering Calculus Notes 303 - y 2 − φ x,y 2 = 1 and...

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

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
This is the end of the preview. Sign up to access the rest of the document.

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

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern