mat186dec07 - University of Toronto FACULTY OF APPLIED...

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University of TorontoFACULTY OF APPLIED SCIENCE AND ENGINEERINGSolutions toFINAL EXAMINATION, DECEMBER, 2007First Year - CHE, CIV, IND, LME, MEC, MMSMAT 186H1F - CALCULUS IExam Type: ASURNAME:GIVEN NAMES:STUDENT NUMBER:SIGNATURE:Examiners:D. BurbullaS. CohenA. EsterovR. HolowinskyF. RochonBreakdown of Results:546 students wrote this exam. The marks ranged from6% to 99%, and the average was 59.9%. Some statistics on grade distributions arein the table on the left, and a histogram of the marks (by decade) is on the right.Grade%Decade%90-100%5.3%A16.7%80-89%11.4%B18.5%70-79%18.5%C17.6%60-69%17.6%D18.3%50-59%18.3%F28.9%40-49%12.3%30-39%8.2%20-29%5.5%10-19%2.7%0-9%0.2 %Page 1 of 11
1. What is the equation of the tangent line to the graph off(x) =exat the point(x, y) = (0,1)?
2. The arc length of the curvef(x) = 2 cosxfor 0xπ/2 is given by
3. How many asymptotes – horizontal, vertical, or slant – are there to the graphofy=x+ 2-2x-2x2+ 2x-3?
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