review_01 - Exam Course Due Date Instructor 16s MATH 2451...

This preview shows pages 1–6. Sign up to view the full content.

Exam : 16s MATH 2451 review 01 Course : Multivariable Calculus Due Date : 2099-02-11 (Wed) Instructor : McCary T.C. Use (First Name) (Last Name) 2016-02-15 02:58

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
1. (10 points) You’ll have to prove Fermat’s theorem in the R R case in the oral exam. You’ll have to prove Fermat’s theorem in the R n R case on the written exam (which is a straightforward consequence of the R R case).
2. (10 points) The proof of Clairaut’s theorem will be a bonus question on the exam.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3. (10 points) Suppose G x y = 0 and that y is an implicit function of x : y = f ( x ). Show dy dx = - ∂G/∂x ∂G/∂y where ∂G ∂y 6 = 0. Hint : consider the function p ( x ) = x f ( x ) , the composition ( G p )( x ) = 0, and the chain rule. This is the reason implicit differentiation from scalar calculus works.
4. (10 points) In this exercise, we’ll arrange a situation where ∂y ∂x ∂z ∂y ∂x ∂z = - 1. (a) Assume a surface S given as the zero level set of a function F : F x y z = 0.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the 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