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

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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
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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 .
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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.
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