211-rossmanith-07faex01-v1

# 211-rossmanith-07faex01-v1 - Date: Oct. 5th, 2007 ' Page...

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Unformatted text preview: Date: Oct. 5th, 2007 ' 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 307 308 309 310 311 Mueller Rui Meyer Rui Konate 1:20pm 2:25pm _ 2:25pm 3:30pm 3:30pm Problem I Points Possible I Total 100 Date: Oct. 5th, 2007 ' Page 2/8 1. (14 points) Coneitier the function ﬁr) = sci/3. (a) (4 points) Use the linear approximation to estimate (6)” (b) (4 points) Use the linear approximation to estimate (10)”? (c) (2 points) Compute 11m f (d) (2 points) Compute 1imf’(x). 3—)00 (e) (2 points) Compute 1imf”(a:). I \$—’OO N) Date: Oct. 5th, 2007 Page 3/8 2. (14 point—sujhrConsider a particle moving along theﬁaxis “Ea'lfnnction of time according to the formula:' * 5(t) = 253 —~ 7.57:2 + 12: for 222 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. (6) (2 points) Find all the time intervals when the particle’s velocity is in creasmg. (f) (2 points) Find all the time intervals when the particle’s velocity is de» creasmg. Date: Oct. 5th, 2007 Page 4/8 3. ( 14 points) C'ohhsﬂiudrer the function = Vim—+6 for :c _>_ —-E—. a (a) (2 points) Find a formula for the slope of the secant line through the points (x,f(x)) and (a: + h,f(:c + (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 (:27, f (c) (6 points) Write the equation of the tangent line at the point Where m =2 2. Date: Oct. 5th, 2007 Page 5/8 4. (14 points) Consider the function f (x) = 22:5. (a) (2 points) Find a formula for the slope of the secant line through the points (x,f(:z:)) and (m + h, f(a: + h)). (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 (x, f (c) (6 points) Write the equation of the tangent line at the point Where a: = O. Date: Oct. 5th, 2007 Page 6/8 5. (14 points) You’invest \$123.45 into a bank account that pays agyﬂearly 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? (c) (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 ln(36) years? 0: Date: Oct. 5th, 2007 Page 7/8 6. (14 points) Soﬁa/é each of the following equatibns: (a) (2 points) 1n(a:5) = 25 (b) (4 points) In + -— 1n = O (c) (4 points) 62”” — 66”” + 5 = 0 (d) (4 points) In (e‘” +, 11113) = x Date: 0013. 5th, . Page W 7. (14 points} Co’néider the function: :52 — 3a: — 10 “56) ﬁ 22:2 + 6x —— 20' Find any vertical and horizontal asymptotes and determine Where the function is negative or positive and howthe graph approaches each asymptote. Sketch the graph of f (:6) using that information. ...
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## This note was uploaded on 08/08/2008 for the course MATH 211 taught by Professor Onlineresources during the Fall '06 term at University of Wisconsin.

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211-rossmanith-07faex01-v1 - Date: Oct. 5th, 2007 ' Page...

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