Midterm 2016 Math 209 - MATH 209/2 all sections except EC...

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Unformatted text preview: MATH 209/2 all sections except EC: - Fundamental Mathematics II Midterm - October 2016 (1h30min) Only approved calculators are permitted. MARKS [7] 1. (a) Find lim ———V"”+25_5. w—w {B [7] [7] [12] [7] [10] [10] [10] (b) Give functions f (m) and g(:c) with the following properties: (1) game) = o (n) 39(2) = o (in) 1.3. % = :3; 2. Let h(:z:) = 7 — :33. won. out the following in detail: n. [Mac + s) — h<w>1 5-)0 S - 3. (a) If f(:c) = —4:1;2’3 + 5, find f’(1). Do not simplify. (b) If g(:z:) ; (211:3 — 4) [ln(:c2) + 3], find 9’ (2). Do not simplify. (c) Find h’(:z:) if h(:z:) = {—fl-Tmfi (d) Find the value of dy if y = $3 + 2,:1: = 3 and the change in a: is 0.4. 4. A population grows from ten million to thirty million in ten years. Find the associated annual rate of growth assuming that it is compounded continuously. 5. The cost of printing as books is given by the function C(23) = 20,000 + 102:. (a) Find the average cost per unit if 2000 books are produced. (b) Find the marginal average cost when 2000 books are produced and interpret the results. (0) Use (a) and (b) to estimate the average cost per unit if 2001 books are produced. 6. Find m’ for a: = 27(1)) defined implicitly by 1+:t1np = 126‘” and evaluate as’ at (p, (1:) = (1,0). 7. A point is moving along the :1: axis at a constant rate of 5 units per second. At which point is its distance from (0,1) increasing at a rate of 2 units per second? At 4 units per second? At 5 units per second? At 10 units per second? Explain. 5', _ ' (30,) == «10, 000 + /0,,o- A“ _. ,, , . Cab—3 —— 59:2 , 520/000+/0/Xr$ @2930} 440 £14“ = @000 I N m ,0.005 V 6&000 ,(‘j /?. 7?5‘. 066 <2 062‘: aw w 0% f’f/ 7746042050151 90?,“ ’00— Q~-'__..—-——-— 5 ...
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