mat237 prob set 2 - University of Toronto DEPARTMENT OF...

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University of Toronto DEPARTMENT OF MATHEMATICS MAT 237y1y Assignment #2 Due date: October 15, 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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ASSIGNMENT #2 1. (a) Parametrize by a continuous map f the polygonal curve L from 3 ] 1 , 0 [ : R S (0, 0, 0) to (2, 1, 1) to (2, 3, 2) to (3, 3, 3). (b) Find the intersection point P 0 of the plane 1 2 2 = + z y x and the polygonal curve L. (c) Write the equation of the plane Π that contains the point P 0 and the tangent line to the curve at the point (0, 2, 0). ) 1 , 1 , 1 ( ) ( 3 2 + + + = t t t t g 2
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2. Given are the following subsets of the Euclidean space 2 R : } 1 0 : ) 0 , {( 1 < = x x S } 1 0 , ,... 3 , 2 , 1 : ) , 1 {( 2 = = y n y n S and )} 2 / 1 , 0 {( 3 = S . Consider the sets and .
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