probset 3 - University of Toronto DEPARTMENT OF MATHEMATICS...

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_ _ University of Toronto DEPARTMENT OF MATHEMATICS MAT 237Y1Y Assignment #3 Due date: November 05, 6:10p.m Last Name: ____________________________ First Name: _____________________ Student #: _____________________________ Lecture Section: ______________ (a) TOTAL MARKS: 50 (b) WRITE SOLUTIONS ON THE SPACE PROVIDED, USE THE REVERSE SIDE OF A PAGE TO CONTINUE IF NECESSARY. (c) DO NOT REMOVE ANY PAGES. THERE ARE 6 PAGES (d) FOR A FULL MARK YOU MUST PRESENT YOUR SOLUTION CLEARLY MARKER'S REPORT Question Mark 1 /10 2 /10 3 /10 4 /10 5 /10 TOTAL /50 1

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1. (a) Suppose is differentiable and let R R f 2 : ) sin , cos ( ) , ( θ r r f r F = . Calculate 2 2 2 ) ( 1 ) ( + F r r F in terms of the partial derivatives of . ) , ( y x f (b) Suppose is differentiable and R R f 2 : x f c t f = for some nonzero constant c . Prove that for some function h . ) ( ) , ( ct x h t x f + = HINT: Let . ) , ( ) , ( ct x x v u + =
2. (a) If and x and y are functions of

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probset 3 - University of Toronto DEPARTMENT OF MATHEMATICS...

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