problem_set_7

# problem_set_7 - Name Section Student ID Last First MI Math...

This preview shows pages 1–4. Sign up to view the full content.

1 Name: First MI Last Student ID # Problem Set #7 Score Section: C REDIT 2 1 0 Problem #2 . A particle moves in the plane according to x = f ( t ), y = g ( t ). Find the formula for the rate at which the particle moves away from the origin and show that, in general this is not | r v | (where r v is the velocity vector). C REDIT 2 1 0 Problem #1 . Let F ( x , y , z ) denote a function of three variables. Suppose that the surface F ( x , y , z ) = c (with c a constant) allows an implicit definition of a function y = y ( x , z ). Obtain an expression for y x in terms of the partial derivatives of F . Math 32A Lecture #5 Fall 2007

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

View Full Document
2 Problem Set #7 C REDIT 2 1 0 Problem #4 . Let F ( x , y , z ) denote a function of three variables. Assume that at some points on the surface F ( x , y , z ) = c (with c a constant) it is possible to define three implicit function, z = z ( x , y ), x = x ( y , z ) and y = y ( z , x ). Show that under these circumstances, the (somewhat mysterious) relationship holds: z x y z x y = –1. C REDIT 2 1 0 Problem #3 . Consider the points ( x , y , z ) where yz = log( xz + z 2 ). Assuming that this relation can be used to define a function z = z ( x , y ) at some of these points, and that the point ( x 0 , y 0 , z 0 ) is one such point, compute the partial derivatives z x and z y at this point expressing your answer in terms of x 0 , y 0 & z 0 .
3 Problem Set #7 C REDIT 2 1 0 Problem #6 . A particle moves in the xy –plane according to x ( t ) = t + 2t 2 , y ( t ) = cos π t ; 0 ≤ t ≤ 1.

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