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Unformatted text preview: MAC 2311 CALCULUS WITH ANALYTIC GEOMETRY ONE
TEST 2 Ou’i’ of
Name S Score 50 Directions: Answer each question, showing ALL your work for full credit. 1. Calculate the derivative of each of the following functions. (8 points) f (x) = 7: 2x + é—x6 — «5 (Reduce any fractions in the ﬁnal answer) g(x) = —x’4 + 5 V; (Express answer in radical notation with no negative exponents) h(x) = x2 sinx + 2x cosx — 25inx (Simplify completely by combining like terms) b] (X): 33X MAX +XD‘COSX +RcorXstsnx Q Cosx k(x) = sec(x2) Valencia Community College 2. Let f and g be functions whose graphs are shown below. Suppose that P(x) = f (x)  g(x) and
C (x) = f (g(x)). Calculate, step by step, the values of P’(2) and C '(2). (6 points) Valencia Community College Find the equation of the tangent line to the graph of y = \/ tanx at x = E. U 4 se EXACT answers
involving “pi” in your ﬁnal response. (5 points) ‘
{5% 3:: L. Secax L/ ﬂag. in x: 1
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get :: {a 2 z 3}— Valencia Community College . A particle moves along a straight line whose position at any time is given by the equation 1 . . .
s = 1— 5 t + 3t2 — 313 where t Z 0 , 2‘ IS measured 1n seconds and 5 1n feet. Answer the following questions. Be careful of signs. a) When is the particle moving in the negative direction? (2 points) M4540
my“ ..
' “r5 v: awe6:0 b) c) What is the total displacement of the particle during the ﬁrst 6 seconds of travel? (1 point) 5305"“503‘): $~l =§6~tté d) What is the total distance traveled by the particle during the ﬁrst 6 seconds? (2 points) Valencia Community College Sm (XHA == weasg M’m
(“Ema fﬁé r K, 1 0‘3
Cos(x+ g)[i+ 3%} = (B £039, + XE 8m?) .332
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Cos (x+e.)—\ chs j; 7(3ij ~ 0‘9 + $3 QosQQig) = C053 “503(X’f3)
33: cm @W a; ’ xsing + COSDH’SB Valencia Community Coilege 6. For What values of x on the interval [0,47r] does the graph of f (x) = Xx/E — 2cosx have a horizontal tangent? Note: you are going around the unit circle twice. Use EXACT answers
involving “pi” in your ﬁnal response. (6 points) $00: $5 +Qs‘m'xzo 9w”: 4:; saw is maeler ‘m "toadmwlsilll: cmlm
“a , Valencia Community College x k
7. The derivative of f (x) = can be written in the form f ’(x) = where k and m
\j x 2 + 4 (x2 + 4)“
are real numbers. Find the exact values for k and m . (6 points)
43 ' (X\= (M XqHl — (543% Q R
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XR+L\ (XORLl} Q (xiii—if 9‘ Valencia Community College 8. The surface area of a sphere is increasing at a rate of 3768 cm2 per second. Find the rate at
which volume of the sphere is increasing when the equator of the sphere is 314 cm ? (6 points) The volume of a sphere in terms of its radius is V = g7: r3 The surface area of a sphere in terms of its radius is A = 47: r2 Note: For simplicity, use the number 3.14 as an approximation for “pi” in ALL of your
calculations. Be sure to include the units of measurement in your ﬁnal answer. ;\ om“
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 End of Test————— Valencia Community College ...
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This note was uploaded on 10/18/2011 for the course MAC 2311 taught by Professor Jameslang during the Fall '11 term at Valencia.
 Fall '11
 JamesLang
 Calculus, Geometry

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