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Unformatted text preview: Date: Oct. 5th, 2007 O Page 1/8 MATH 2111
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 thEEaxis 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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 Fall '06
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 Calculus

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