# mat186apr08 - University of Toronto FACULTY OF APPLIED...

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Chapter 7 / Exercise 20
Algebra and Trigonometry: Real Mathematics, Real People
Larson
Expert Verified
University of TorontoFACULTY OF APPLIED SCIENCE AND ENGINEERINGSolutions toFINAL EXAMINATION, APRIL, 2008First Year - CHE, CIV, IND, LME, MEC, MMSMAT 186H1S - CALCULUS IExam Type: ASURNAME:GIVEN NAMES:STUDENT NUMBER:SIGNATURE:Examiner:D. BurbullaComments:1. This exam was very similar to the exam of Dec 07. The main differences were:no related rates problem, and an area problem instead of a graphing question.2. If you set up the area problem by integrating with respect tox,you have tointegrate lnx,which we haven’t done yet. But you can find the integral bylooking at the area with respect to they-axis.3. In the last problem, to confirm the critical point is a minimum point, it iseasier to compare the length at the endpoints with the length at the criticalpoint. The second derivative is quite messy.Breakdown of Results:99 students wrote this exam.The marks ranged from25% to 94%, and the average was 60.6%. 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%1.0%A6.0%80-89%5.0%B16.2%70-79%16.2%C34.3%60-69%34.3%D25.3%50-59%25.3%F18.1%40-49%12.1%30-39%5.0%20-29%1.0%10-19%0.0%0-9%0.0%Page 1 of 10
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Chapter 7 / Exercise 20
Algebra and Trigonometry: Real Mathematics, Real People
Larson
Expert Verified
1. What is the equation of the normal line to the graph off(x) =exat the point(x, y) = (0,1)?