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Unformatted text preview: MA 165 EXAM 3 Fall 2008 Page 1/4
NAME
Page 1 /20
[—
10—digit PUID , . Page 2 /40
. . P 3 16
RECITATION INSTRUCTOR age /
' Page 4 / 24
DIRECTIONS
1. Write your name, 10digit PUID, recitation instructor’s name and recitation time in PC): the space previded 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 shew suﬂicient work to justify all answers unless otherwise stated in the
problem. Correct answers with inconsistent work may not be given credit. Please.
Write neatly. Remember, if we cannot read your work and follow it logically, you may receive no credit.
Credit for each problem is given in parentheses in the left hand margin.
No bucks, notes, calculators, or any electronic devices may be used on this exam. Find the absolute maximum and absolute minimum values of thefunction
f (x) = (x2 — 3)e“” on the interval [0, 4]. ' Find a11__numbers c thatsatisfy the conclusion of the Mean Value Theorem for the ' 5.
6.
(10) 1.
(19)“W2L, function f = 11:3 — 611: on the interval {—2, 2]. l MA 165 EXAM 3 Fall 2008 Page 2/4 Name: (30) 3. Find each of the following as a real number, +00, —00, or write DNE (does not exist). . m+sinm
(a) 11m —.
xao :z:+cos:v cos :1:
1', .
(b) Mlély 1 — sinx , , 1 ~coszt:
(‘0 £35 T
(d) 311330 (My (e) I Ilim (1 + 2x)? z——)O+ (10) 4. If 1’200cm2 of materialis available to make a box with square base and an open top,
ﬁnd' the largest possible volume of the box. (Let a: be the length of an edge of the
baSe and y be the height). MA 165 EXAM 3 Fall 2008 Page 3/4 Name: (16) 5. Let f(:1:)= function on the axes below. Give both coordinates of the intercepts, local extrema
and points of inﬂection, and give an equation for each asymptote. Write NONE Where
appropriate. Give all the requested information and sketch the graph of the intercepts  symmetry
horizontal asymptotes
vertical asymptotes intervals of increase ::
::
::
::
intervals of decrease
intervals 'of concave down intervals of concave up MA 165 EXAM 3 Fall 2008 Page 4/4 Name: (10) 6. Find the area of the largest rectangle that can be inscribed in a right triangle with
legs of lengths 3cm and 4cm if two sides of the rectangle lie along the legs. (Place the
vertices of the triangle at the points (0, 0), (4,0) and (0, 3) of the (11:, y)—plane). S i 7. A particle moves in a straight line and has acceleration given by a(t) = sin t. Its initial velocity 12(0) ‘2: 0 and its initial position is 5(0) 2 0. Find its position function s(t). s(t) = 10
H 8‘. Evaluate the integral / la: — 5dx by interpreting it in terms of areas.
0 , I ' 9. Find the most general antiderivative of f = V4 x3 + v3 1:4. ...
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This note was uploaded on 09/14/2011 for the course MA 165 taught by Professor Bens during the Fall '08 term at Purdue.
 Fall '08
 Bens
 Calculus, Geometry

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