112FinalAF09Solutions

112FinalAF09Solutions - Math 112(Calculus I Final Exam Form...

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Math 112 (Calculus I) Final Exam Form A KEY Multiple Choice. Fill in the answer to each problem on your computer-scored answer sheet. Make sure your name, section and instructor are on that sheet. 1. Approximate Z 5 1 x 4 dx using a Left Hand sum with 2 subintervals (n=2). (a) 82 (b) 164 (c) 81 (d) 162 (e) 624 (f) 625 (g) None of these 2. Find the area under the function f ( x ) = 3 x from x = 1 to x = 8. (a) 45 4 (b) 1 4 (c) 12 (d) 15 (e) 1 12 None of these 3. Given the limit statement lim x 1 (2 x - 3) = - 1 pick the largest δ that works with the deﬁnition of the limit if ± = 0 . 06. (a) 0.001 (b) 0.005 (c) 0.01 (d) 0.02 (e) 0.03 No such δ exists 4. Which of the following is an inﬂection point of f ( x ) = x x 2 + 1 ? (a) 1 (b) - 1 (c) 2 (d) - 2 (e) 2 - 2 (g) - 3 (h) 3 5. Given x ln y - y ln x = e 2 - 2 e , ﬁnd dy dx at the point ( e 2 ,e ). (a) 0 (b) e (c) e 2 (d) 1 - e e 2 (e) 1 - e e 2 - 2 e e 2 - 2 e (g) e - 1 e 2 6. Which of the following are x -values for which f ( x ) = sin( x ) - x has a local maximum? (a) - 2 π (b) - π (c) 0 (d) π (e) 2 π More than one of these (g) None of these 7. Which of the following functions has a discontinuous ﬁrst derivative? (a) sinh( x ) (b) x 1 / 3 (c) tan - 1 ( x ) (d) x 1 + x 2 (e) ln( x 2 + 1) All of the ﬁrst derivatives of these functions are continuous 8. d dx Z 2 x 1 1 + t 3 dt =

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a) p 1 + (2 x ) 3 - 2 b) 2 p 1 + (2 x ) 3 - 2 c) 1 + x 3 - 2] d) 2 1 + x 3 - 2 e) p 1 + (2 x ) 3 f) 2 p 1 + (2 x ) 3 g) 1 + x 3 h) 2 1 + x 3 Solution: Short Answer: Fill in the blank with the appropriate answer.
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112FinalAF09Solutions - Math 112(Calculus I Final Exam Form...

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