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Unformatted text preview: MAT 284 Spring 2005 NAME: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
SIGNATURE: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
SUID: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Final Exam UC 1 Read each question carefully. Budget your time so you have the opportunity to attempt
each question. There are 13 questions and the duration ofthe exam is 2 hours.
Ambiguous or illegible answers and answers without work will not receive full credit. Problem Number % Possible Points Score 1 1O 4'
2 1O
3 A 10 +__ F 4 10 M
5 ﬂl 10 +
6 A 10 L 7 10 W
8 r 15 k 9 a 10 +
10 10
11 Y 10 A
12 1O
13 40 5’ 4 v TOTAL h 436 ISO . . . I . . 1. leferentlate the functlon s = In M’— (you need not 51mp11fy your answer)
63! 51(z +11)2 3 (10 points) 2. The marginal revenue function for a product is — 7(q ~ 45) , Find the demand function for the product.
(10 points) 3. Evaluate the following limits where possible otherwise stating they do not exist. . 4x+x2—21
a Inn—‘—
()Hw12w7x+x2 (2 points) . 4 2—2
(b)11m_x:£__?1
H312—7x+x (3 points) 1 (C)lin210gb(x+hjh X
(5 points) 4. Evaluate f’(x) when (complete simpliﬁcation is not necessary)
(a) J dx = x3 +55x€ + 62 (5 points) (b) f(x) = x/xz + 5 (3 points) 3
X (C) f(x)=5 2 ‘X (2 points) 5. Supply and demand equations for a certain product are
25q + p — 2050 = O and — 40q + p + 3150 = 0 respectively, wherep represents the price
per unit in dollars and q the number of units sold per time period. (a) Find the equilibrium price algebraically. (5 points) (b) Find the equilibrium price after a tax ofSO dollars is imposed on the supplier. (5 points) 6. Suppose y = 6””)2 (x — 2)2. (3) Given y is the composition oftwo functions y : (f o g)(x) what could f(x) and
g(x) possibly be? NOTE: Neither f nor g is the function x. (3 points) (b) Usmg this information ﬁnd 61,—) (you need not Simplify your answer).
x (7 points) 7. The curve C is given by the equation y z x2  4x + 3.
(21) Find the equation ofthe line tangent to the curve C when x 2 —5 (5 points) (b) Is this line perpendicular to the line y : ﬁx — 14 ? Give a reason why or why not. (5 points) 8. Evaluate the indeﬁnite integrals 2 2
3— d
(20% V?) x (10 points) X (b) dx (5 points) 9. Sketch the graph ofthe function y = 4x3 — 3xA stating clearly where it is increasing and decreasing, concave up and concave down and labeling all intercepts, relative maxima
and minima and inﬂection points. SHOW ALL YOUR WORK (10 points) 10. Verify ﬂ = p dq (10 points) [ 1+1 ’7 J 00
when p = ~3— — 10. SHOW ALL YOUR WORK. q l l. A speaker manufacturer is currently able to sell 100 car speaker sets at a price of$l20
per set. Assuming elasticity of demand for car speakers sets is approximately l.2 and the
price were dropped to $85, how many sets could the manufacturer sell now? (10 points) 12. A theatre wishes to purchase a speaker system. The manufacturer has speaker systems
with anywhere from 50 to 100 speakers. The cost of each speaker is listed as $35,
however, for each additional speaker above 50, there is a discount of 50 cents on the cost
per speaker. What quantity of speakers will minimize cost for the theatre? (10 points) 13. Given 10g3 5 = k ﬁnd an expression for 10g3 in tenns ofk. (SHOW YOUR WORK). (5 points) ...
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 Spring '11
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