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Unformatted text preview: MA 165 EXAM 2 Fall 2006 Page 1/4
NAME Page 1 / 16
10DIGIT PUID Page 2 /32 l Page 3 / 28
RECITATION INSTRUCTOR Page 4 / 24
RECITATION TIME TOTAL /100 DIRECTIONS I. O0 (16) 1. Write your name, IO—digit 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. The test has four (4) pages, including this one. . Write your answers in the boxes provided. 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. Credit for each problem is given in parentheses in the left hand margin. . N0 books, notes or calculators may be used on this exam. Find the derivative of the following functions. (It is not necessary to simplify).
(a) y = 6—5:: cos(3a:). (c) y = ln(1 + 263$). (d) f(:1:) = \3/9 + 8sin2x (8) (12) (12) MA 165 EXAM 2 Fall 2006 d
2. Find d—y by implicit differentiation, if (tan y)(sin x) = my.
11" Page 2/4 3. Find the exact value of each expression.
(a) sinHg) (b) sin(sin_1 0.7) (c) tan—1(tan 4—7') (d) cos‘1(—%) WW 4. Find the derivatives of the following functions. (It is not necessary to simplify). (a) y = tan” x/E (b) f (a?) = sin1W2) (C) 2/: (33+ 1V” MA 165 EXAM 2 Fall 2006 1
x—l' (8) 5. Find a formula for f(")(x) if f(ac) = Page 3/4 (4) 6. Find an equation of the tangent line to the curve y = sinhx at the point (0,0). (6) 7 If FCC) = f(9($)), f’(1) = 5, and 9(55) = 621, ﬁnd F’(0) me) = (6) 8. Find the linearization L(a:) of the function f (11:) = (sing: + cos 3:)3 at a = (4) 9. Find the differential dy if y = sec(5:r:). MA 165 EXAM 2 Fall 2006 Page 4/4 (12) 10. Air is let out of a spherical balloon so that its surface area is decreasing at a rate of 2 cm2 / sec.
Find the rate at which the radius of the balloon is decreasing when the radius is 20 cm. (12) 11. A lighthouse is located on a small island 3 km away from the nearest point P on a straight
shoreline and its light makes four revolutions per minute. How fast is the beam of light moving
along the shoreline when it is 1 km from P? ...
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 Fall '08
 Bens
 Calculus, Geometry, Derivative, Following, Lighthouse

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