practice test 2

# practice test 2 - 11 meters away from the nearest point on...

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MAT 111 Practice Test 2 No calculators allowed Spring 2010 1

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1. (10 points) Find the equation of the tangent line to 2 x + 2 y = 1+ x 2 y 2 at the point (1 , 1). 2
2. (30 points) Evaluate the following: (a) lim x 2 x 4 - 2 x - 12 x - 2 (b) Find f 0 ( x ) if f ( x ) = sec 3 x 1+sin x 3

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(c) Find f 0 ( x ) if f ( x ) = sin 2 ± x x 3 +1 cos x +2 ² . 4
3. (25 points) Assuming that the earth is located at the point (2 , 0), a comet is observed to be moving along a parabolic path given by y = x (when the distance is measured in units of million km). It is observed that the x co-ordinate of the comet is changing at 3000 km/s. (a) How fast is the distance between earth and the comet changing, when the comet is at (1 , 1). (b) A telescope on earth is constantly tracking the comet. How fast is the telescope rotating, when the comet is at (1,1) ? This problem is almost identical to Problem 20 from Section 2.8 which was on the homework. 5

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4. (25 points) A runner (Let’s call him C) is running around a 400m running track (a real one this time), shown in the ﬁgure below, at 7m/s. His coach Tom is standing
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Unformatted text preview: 11 meters away from the nearest point on the track as shown in the ﬁgure, recording the run on a handicam for analysis later (and for posting on youtube). Assume that (100 /π ) ≈ 33 (for ease of calculation) and answer the following. (a) How fast is the distance between Tom and C changing, when C is 33 meters away from Tom. (This is the rate at which the zoom on the camera needs to be adjusted to maintain a full frame close up of C). (b) How fast should Tom be turning to keep C in frame, when C is at the point P shown. This problem is really two problems that were discussed in class. Part a) is the same as Problem 37 in Section 2.7 and Part b) is the same as Problem 26 from the same section. 6 5. (10 points) Find the approximate value of tan(51 ◦ ) using linear approximation at x = 45 ◦ . 7...
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## This note was uploaded on 12/01/2010 for the course PSY 110 taught by Professor Winters during the Spring '08 term at University of Miami.

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practice test 2 - 11 meters away from the nearest point on...

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