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Unformatted text preview: MA 165 EXAM 2 Fall 2004 Page 1/4
NAME STUDENT ID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. 00 (16) 1. Write your name, student ID number, 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.
. No books, notes or calculators may be used on this exam. Find the derivatives of the following functions. (It is not necessary to simplify).
(a) y = (1 + cos2 x)6. (b) m2) = sinless) (c) = (1 + 31:2)tan’1 9:. (d) y = ln(sin $2) MA 165 EXAM 2 Fall 2004 Page 2/4 (6) 2. Find an equation of the tangent line to the curve 1/3 — x2 = 4 at the point (2, 2). E: (9) 3. If xsiny + cos 2y 2 cos y, ﬁnd (1—3: by implicit differentiation. (6) 4. Find the ﬁrst and second derivatives of the function h(:r) = 9:2 + 1. (8) 5. Find the derivative of the function y = (1n MA 165 EXAM 2 Fall 2004 Page 3/4 (9) 6. Find the exact value of each expression. (a) sinleg) (b) tan‘1 1 (c) sin(cos_1 %) , . 6
(6) 7. Find the differential of the function y = . :1:—1 (10) 8. (a) Find the linearization L(a:) of the function f = ﬂ at a = 1. L(:z:) = (b) Use a linear approximation to estimate the number V1.1. x/ﬁ 22 (6) 9_. Suppose that a: and y are functions of t and are related by the equation 1:2 + y2 = 1.
dy __ d1: _ 1 1
If a — —2, ﬁnd a when (13,31) —— (W, E . MA 165 EXAM 2 Fall 2004 Page 4/4 (12) 10. Gravel is being dumped from a conveyor belt at a rate of 30 ft3 / min and its coarseness
is such that it forms a pile in the shape of a cone whose base diameter and height are
always equal. How fast is the height of the pile increasing when the pile is 10 ft high? (12) 11. A balloon was released at point A on level ground and is rising at a rate of 140 ft / min.
The balloon is observed by a telescope located on the ground at point B which is 500 ft
from point A. How fast is the telescope’s angle of elevation changing when the balloon
is 500 ft above ground? ...
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 Fall '08
 Bens
 Calculus, Geometry, Derivative, $2, 1 %, recitation instructor, 10 ft, Recitation Time

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