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Unformatted text preview: CONCORDIA UNIVERSITY
Department of Mathematics & Statistics Course Number Section(s)
Mathematics 209 All
Examination Date Pages
Final December 2008 3 Instructors M. Amir, A. Atoyan, F. Balogh, L. Dube
T. Hughes, R. Mearns, R. Raphael, J. Ruddy Course Examiner R. Raphael Special Instruct ions l>
D Ruled booklets to be used.
Only approved calculators are allowed. MARKS [11] 1. [5] 2. Using the deﬁnition of the derivative lirn . . . 4:133 — 2m + 5
<1) Find 33%.. m (ii) Given lim ﬂan) : —5 and lim 9(93) : 4, ﬁnd (a) gig [~2g<m>] (b) 533.) [—wa (iii) Find the value of each of the following: . :32 ~25 . {CZ—323+2
(a) ail—E15 (a: — 5) (b) :lI—{Ila (x — 1)
f(a+h) — m) = 41:3 + 5. ’HO h [14] 3. Do not simplify answers. (a) If f(;r) : 3x15 — 4:1:3 + 6, ﬁnd f’(x).
(b) If f(x) = (m3 — 2302 + 1x333? — 7), ﬁnd f’(;c). (c) hm W) * f(:v)l I x—>3 f(a) , ﬁnd the derivative if MATH 209 Final Examination 3. (Continued) (e) If y : ln[(3m2 + m, then 33 — '2
x
1
(f)Ify= ,thengg2‘7 [3] 4. Find 3/ given $2243 2 400269 + 5. [11] 5. The total proﬁt (in dollars) from the sale of ac lawn mowers is 03mg 1,000 P(.T) 2 30m — 003$2 — 750, (a) Find the average proﬁt per mower if 50 mowers are produced.' December 2008 Page 2 of 3 (b) Find the marginal average proﬁt at a production level of 50 mowers, and interpret the results. (c) Use the results from parts (a) and (b) to estimate the average proﬁt per mower if 51 mowers are produced. [11] 6. Suppose that for a company manufacturing transistor radios, the cost, revenue and proﬁt equations are given by
C’ : 5,000 + 2:0
R = 103: ~ 0.001002 where the production output in 1 week is a: radios. If production is increasing at
the rate of 500 radios per week when production is 2,000 radios, ﬁnd the rate of increase per week in
(a) Cost; (b) Revenue; (c) Proﬁt. MATH 209 Final Examination December 2008 Page 3 of 3 [11] 7. Compute the following:
(a) /3m3($4 + 5)3 d3: (b) / {1/33—3da: (c) /\/——1_3_—_g;dzc (d) / ln(5cc) d3: .CL’ (e) /(2a:+ $2) e<3m2+m3) dm [7] 8. Use the price—demand equation to determine Whether demand is elastic, is inelas
tic, or has unit elasticity at the indicated values of p for Cc=f(p)=1,875—p2
(a) 17:15 0?) 19:25 (C) 19:40 [4] 9. HOW long will it take money to triple if it is invested at 5.5% compounded con—
tinuously? [11] 10. Find the area bounded by f(a:) : :02 — m and g(a:) : 2:6, for —2 g :r; g 3. [12]11. Let ﬁx) : 3:4  2:33.
(a) Find Where f(:c) is increasing, is decreasing, and has local extrema. (b) Find Where f(:E) is concave up, is concave down, and has points of inﬂection. (c) Graph f(x). ...
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