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Math_137_Winter_2010_Midterm_1_Solutions

# Math_137_Winter_2010_Midterm_1_Solutions - Name(Print UW...

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Name (Print): UW Student ID Number: University of Waterloo Term Test 1 Solutions Math 137 Calculus 1 for Honours Mathematics Date: February 22, 2010 Time: 7:00 p.m. - 8:50 p.m. Number of pages: 8 Test type: Closed Book (including cover page) Circle your section number Instructor Section Lecture Time Shengda Hu 001 (8:30 a.m. - 9:20 a.m.) Paula Smith 002 (11:30 a.m. - 12:20 p.m.) Paula Smith 003 (10:30 a.m. - 11:20 a.m.) Instructions 1. Write your name and ID number at the top of this page. Please circle your section num- ber up above. 2. Answer the questions in the spaces provided, using the backs of pages for over±ow or rough work. 3. Show all your work required to obtain your answers. FOR INSTRUCTOR’S USE ONLY Question Mark 1 /8 2 /10 3 /6 4 /13 5 /20 6 /14 7 /7 8 /7 9 /8 10 /7 Total /100

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1. Find the asymptotes of the graph of y = f ( x )where f ( x )= e x + e x e x e x . Solution: The domain of the function f ( x )i s e x e x 6 =0 ,n am e ly , x 6 =0 . Th e only possible vertical asymptote will be x =0 . Wecheckit e 0 = e 0 = 1 and for x> 0 ,e x ± e x > 0 It implies that lim x 0 + f ( x )= .Thu s x = 0 is a vertical asymptote. For horizontal asymptotes, we compute the following lim x →∞ e x + e x e x e x = lim x →∞ 1+ e
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Math_137_Winter_2010_Midterm_1_Solutions - Name(Print UW...

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