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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 opentop 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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 Spring '07
 Sullivan
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