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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.
 Fall '06
 OnlineResources
 Calculus

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