211-rossmanith-07faex01-v2

211-rossmanith-07faex01-v2 - Date: Oct. 5th, 2007 O Page...

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Unformatted text preview: Date: Oct. 5th, 2007 O Page 1/8 MATH 211-1 EXAM #1 NAME: CIRCLE YOUR DISCUSSION SECTION: 301 302 303 304 305 306 Gupta Gupta Meyer Virk Mueller Virk 7:45am 8:50am 8:50am 9:55am 12:05pm 2:25pm 307 308 309 310 31 1 Mueller ' Rui Meyer Rui Konate 1:20pm 2:25pm 2:25pm 3:30pm 3:30pm I Points Possible I w 1. (l4 point—eyConsider thefunction: 4x2 — 12x —- 40 fix): anew—20‘ Find any vertical and horizontal asymptotes and determine where the function is negative or positive and how the graph approaches each asymptote. Sketch the graph of f(x) using that information. ' Date: Oct. 5th, 2007 Page 3/8 2. (14 points) Stowe éach of the following equatibfiséu (a) (2 points) 1n(x5) = 2 (b) (4 points) In (x + — 1n = 0 (c) (4 points) 62:” — 66’” + 5 = 0 (d) (4 points) 1n ((5m + 1112:) = ac V Date: Oct. 5th, 2007 Page 4/8 3. (14 pointS) You invest $123.45 into a bank abcddfitniéi‘bayé‘a‘yéany interest rate of 50%. ' (a) (3 points) If the interest rate is compounded 1 times per year, how long does it take to double your initial investment? (b) (3 points) If the interest rate is compounded 2 times per year, how long does it take to double your initial investment? (0) (4 points) If the interest rate is compounded continuously, how long does it take to double your initial investment? (d) (4 points) If the interest rate is compounded continuously, how much is in your account after 1n(100) years? Date: Oct. 5th, 2007 Page 5/8 . , . ., n ,.,._.w_._._..._.._ ,, J 6$2+1‘ 4. (lzlflfioulhtélflCon'sider the function f 2 (a) (2 points) Find a formula for the slope of the secant line through the points (x, f(a:)) and (a: + h,f(:z: + (b) (6 points) Take the limit as h ~> O of your previous answer to find the formula for the slope of the tangent line at the point (27, f (c) (6 points) Write the equation of the tangent line at the point Where x = O. Date: Oct. 5th, 2007 ' Page 6/8 5. {14 pOihté) "Consider the function 6 f(:c)=\/5:c+6 for mz—E. (a) (2 points) Find a formula for the slope of the secant line through the points (9:, f(x)) and (x + h, f(a: + h)). ' (b) (6 points) Take the limit as h —> 0 of your previous answer to find the formula for the slope of the tangent line at the point (x, f (95)). (o) (6 points) Write the equation of the tangent line at the point where as = 2. Date: Oct. 5th, 2007 ' Page 7/8 6. (14 pointsl’ConSider a particle moving along thEE-axis as emigration of time according to the formula: 5(t) = t3 — 7.52:2 + 12t for t2 0. (a) (3 points) Compute the velocity as function of time. (b) (3 points) Compute the acceleration as a function of time. (c) (2 points) Find all the time intervals when the particle is moving to the right. (d) (2 points) Find all the time intervals When the particle is moving to the left. (e) (2 points) Find all the time intervals when the particle’s velocity is in- creasing. (f) (2 points) Find all the time intervals when the particle’s velocity is de- creasing. fl! Date: Oct. 5th, 2007 Page 8/8 7. (1456mm) Consider'the function me) = sci/3. (a) (4 points) Use the linear approximation to estimate (6)1/3. (b) (4 points) Use the linear approximation to estimate (10)1/3. (c) (2 points) Compute lim f(:c). $—’OQ (d) (2 points) Compute lim f’(m).' ' $—’>OC (e) (2 points) Compute lim f” ...
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211-rossmanith-07faex01-v2 - Date: Oct. 5th, 2007 O Page...

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