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Unformatted text preview: MA 165 EXAM 2 (make—up) Fall 2009 Page 1/4 NAME Page 1 / 16
STUDENT ID ‘ Page 2 / 30 P 26
RECITATION INSTRUCTOR age 3 / Page 4 /28
RECITATION TIME [TOTAL AGO DIRECTIONS 1. Write your name, 10wdigit PUID, recitation instructor’s name and recitation time in
the space provided above. Also write your name at the top of pages 2, 3 and 4. 2. The test has four (4) pages, including this one.
. Write your answers in the boxes provided. 4. You must show sufﬁcient work to justify all answers unless otherwise stated in the
problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin.
6. No books, notes, calculators or any electronic devices may be used on this exam. OJ (16) 1. Find the derivatives of the following functions. (It is not necessary to simplify).
(a) y = 63"” cos(4a3) (b) f(t) : \3/—““1 — sint (C) y = tank”) (d) y =1n(Sin(€$)) MA 165 EXAM 2 (make—up) Fall 2009 Name (6) 2. IfF(;v :f g
f’(2)= ,9 (9) 3. Find an equation of the tangent line to the curve 3:2 +y2 : 3y+8 at the point (—2, 4). (9) 4. Find the exact value of (a) (— (b) tan—Kw) (c) sin(2 sin—1%)) (6) 5. Find the diﬁerential dy of each function:
(a) y : wsec(3a:) (b) y = NZ“ MA 165 EXAM 2 (1nake~up) Fall 2009 Name Page 3 / 4 (12) 6. Find the derivatives of the following functions. (It is not necessary to simplify).
(a) y : tan—10:3 + 1) (b) : sin"1 \fi (C) y = 331” ‘ (8) 7. Use a linear approximation to estimate \/ 99.5 C3 (6) 8. If a ball is thrown vertically upward with a velocity of 80 ft / sec, then its height after
15 seconds is s : 80t — 16752. Find the acceleration of the ball when it reaches its
maximum height. ' S (14) 9. A kite 100 ft above the ground is being blown away from a person lyingon the ground ' I i (14) MA 165 EXAM? (make—up) ' Fall 2009’ Name: and holding its string. The kite moves parallel to the ground at a constant height and
in a ﬁxed direction, at the rate of 10 ft /sec. At what rate must the string be let out
when the length of the string that is already let out is 200 ft? ' 10. A spotlight on the ground shines on a wall 100 ft away. A man 6 ft tall starts at the
spotlight and walks directly towards the wall at 5 ft / see. How fast is the length of his
shadow on the wall decreasing when he is 50 ft from the wall? (Let x be the distance
of the man from the spotlight and let y be the length of his shadow on the wall). QP‘aéél‘l/i‘l'» »: ...
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 Fall '08
 Bens
 Calculus, Geometry

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