MidTerm S07

# MidTerm S07 - MAT 102 Spring 2007 1 The Midterm Exam Name...

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Unformatted text preview: MAT 102 - Spring 2007 1 The Midterm Exam March 14, 2007 Name: Instructor: Instructions: You have 90 minutes to complete this exam. Calculators, notes, and collaboration are not allowed. Please show your work, and write legibly. Place a box around your ﬁnal answer for each question. Good luck! Pledge of Honor: Please copy the following and sign. I pledge my honor that I have not violated the Honor Code during this examination. MAT 102 — Spring 2007 Question 1. (10 points) Find the following limits: l—cos 2a: a: (b) limmqgﬂ + 1rx)°°”’ (a) limzﬁo MAT 102 — Spring 2007 Question 2. (10 points) A curve is given parametrically by (C(t) =t1nt, y(t) = sint for t > 0. Compute the tangent line to the curve for t = W. MAT 102 _ Spring 2007 4 Question 3. (15 points) We want to estimate the volume of a cylinder, whose height is known to be 12 ft, by measuring the circumference of its base. The circum- ference is roughly 27F ft. How accurately do we have to measure the circumference if we want to know the volume within an error of l ft3? MAT 102 - Spring 2007 5 Question 4. (15 points) Sketch'the graph of __ a: —x2+1 11(3?) for :1: E (—00, +00). Clearly mark critical points, points of inﬂection and determine the absolute extremes. MAT 102 - Spring 2007 6 Question 5. (10 points) A butterﬂy is ﬂying away from a lamp which is 20 ft tall. At some point, it is 15 ft above the ground and ﬂying at 2 ft/sec horizontally away from the lamp. How quickly is its shadow on the ground moving at that moment? MAT 102 - Spring 2007 7 Question 6. (15 points) You want to design an open-top cylindrical barrel whose surface area (b0tt0m+sides) is 37r ftg. What is the maximum volume of such a barrel? MAT 102 — Spring 2007 Question 7. (10 points) Find the following indeﬁnite integrals: (a) “8‘” + 3:6 + 11:”1)d:c. (b) fﬁ~ MAT 102 - Spring 2007 9 Question 8. (15 points) Ferrari F430 achieves a deceleration of 32 ft 5—2. At a speed of 160 ft s‘1 (= 108 mph), you slam on the brakes. Express the distance traveled from this moment as a function of time 15. How long does it take before the car comes to a complete stop? What is the distance between where you started braking and where you stop? ...
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MidTerm S07 - MAT 102 Spring 2007 1 The Midterm Exam Name...

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