EBK BUSINESS MATH
11th Edition
ISBN: 8220103632072
Author: NOBLE
Publisher: Pearson Education (US)
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Chapter 3.2, Problem 1SE
To determine
To calculate: The sum of an expression
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4) Consider the initial value problem
"
8y +30y+25y = 0, y(0) = -2, y (0) = 8
What is the t-coordinate of the local extreme value of y = y(t) on the interval (0, ∞)? Enter your
answer as a decimal accurate to three decimal places.
Tips
S
ps
L
50.
lim
x2
- 4
x-2x+2
51.
lim
22
-
X
52.
53.
x 0
Answer
lim
x 0
lim
2-5
X
2x2
2
x²
Answer ->
54. lim
T
- 3x
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- 25
+5
b+1
b3b+3
55. lim
X
x-1 x 1
Answer
56. lim
x+2
x 2 x 2
57. lim
x²-x-6
x-2 x²+x-2
Answer->
23-8
58. lim
2-22-2
10) Which of the following is the general solution of the homogeneous second-order differential
equation y + 8y + 52y=0? Here, C, C₁, and C2 are arbitrary real constants.
A) y = C₁ecos(61) + C₂e*sin(61) + C
B) y = et (sin(4t) + cos(6t)) + C
C) y = C₁esin(6) + C₂e+ cos(6t) + C
D) y = C₁esin(6) + C₂e+cos(6)
E) y=e(C₁sin(61) + C₂cos(61))
Chapter 3 Solutions
EBK BUSINESS MATH
Ch. 3.1 - Prob. 1-1SCCh. 3.1 - Prob. 1-2SCCh. 3.1 - Prob. 1-3SCCh. 3.1 - Prob. 1-4SCCh. 3.1 - Prob. 1-5SCCh. 3.1 - Prob. 1-6SCCh. 3.1 - Prob. 2-1SCCh. 3.1 - Prob. 2-2SCCh. 3.1 - Prob. 2-3SCCh. 3.1 - Prob. 2-4SC
Ch. 3.1 - Prob. 1SECh. 3.1 - Prob. 2SECh. 3.1 - Prob. 3SECh. 3.1 - Prob. 4SECh. 3.1 - Prob. 5SECh. 3.1 - Prob. 6SECh. 3.1 - Prob. 7SECh. 3.1 - Prob. 8SECh. 3.1 - Prob. 9SECh. 3.1 - Prob. 10SECh. 3.1 - Prob. 11SECh. 3.1 - Prob. 12SECh. 3.1 - Prob. 13SECh. 3.1 - Prob. 14SECh. 3.1 - Prob. 15SECh. 3.1 - Prob. 16SECh. 3.1 - Prob. 17SECh. 3.1 - Prob. 18SECh. 3.1 - Prob. 19SECh. 3.1 - Prob. 20SECh. 3.1 - Prob. 21SECh. 3.1 - Prob. 22SECh. 3.1 - Prob. 23SECh. 3.1 - Prob. 24SECh. 3.1 - Prob. 25SECh. 3.1 - Prob. 26SECh. 3.2 - Prob. 1-1SCCh. 3.2 - Prob. 1-2SCCh. 3.2 - Prob. 1-3SCCh. 3.2 - Prob. 1-4SCCh. 3.2 - Prob. 1-5SCCh. 3.2 - Prob. 1-6SCCh. 3.2 - Prob. 2-1SCCh. 3.2 - Prob. 2-2SCCh. 3.2 - Prob. 2-3SCCh. 3.2 - Prob. 2-4SCCh. 3.2 - Prob. 2-5SCCh. 3.2 - Prob. 2-6SCCh. 3.2 - Prob. 2-7SCCh. 3.2 - Prob. 2-8SCCh. 3.2 - Prob. 2-9SCCh. 3.2 - Prob. 2-10SCCh. 3.2 - Prob. 2-11SCCh. 3.2 - Prob. 2-12SCCh. 3.2 - Prob. 3-1SCCh. 3.2 - Prob. 3-2SCCh. 3.2 - Prob. 3-3SCCh. 3.2 - Prob. 3-4SCCh. 3.2 - Prob. 3-5SCCh. 3.2 - Prob. 3-6SCCh. 3.2 - Prob. 3-7SCCh. 3.2 - Prob. 1SECh. 3.2 - Prob. 2SECh. 3.2 - Prob. 3SECh. 3.2 - Prob. 4SECh. 3.2 - Prob. 5SECh. 3.2 - Prob. 6SECh. 3.2 - Prob. 7SECh. 3.2 - Prob. 8SECh. 3.2 - Prob. 9SECh. 3.2 - Prob. 10SECh. 3.2 - Prob. 11SECh. 3.2 - Prob. 12SECh. 3.2 - Prob. 13SECh. 3.2 - Prob. 14SECh. 3.2 - Prob. 15SECh. 3.2 - Prob. 16SECh. 3.2 - Prob. 17SECh. 3.2 - Prob. 18SECh. 3.2 - Prob. 19SECh. 3.2 - Prob. 20SECh. 3.2 - Prob. 21SECh. 3.2 - Prob. 22SECh. 3.2 - Prob. 23SECh. 3.2 - Prob. 24SECh. 3.2 - Prob. 25SECh. 3.2 - Prob. 26SECh. 3.2 - Prob. 27SECh. 3.2 - Prob. 28SECh. 3.2 - Prob. 29SECh. 3.2 - Prob. 30SECh. 3.2 - Prob. 31SECh. 3.2 - Prob. 32SECh. 3.2 - Prob. 33SECh. 3.2 - Prob. 34SECh. 3.2 - Prob. 35SECh. 3.2 - Prob. 36SECh. 3.2 - Prob. 37SECh. 3.2 - Prob. 38SECh. 3.3 - Prob. 1-1SCCh. 3.3 - Prob. 1-2SCCh. 3.3 - Prob. 1-3SCCh. 3.3 - Prob. 1-4SCCh. 3.3 - Prob. 1-5SCCh. 3.3 - Prob. 2-1SCCh. 3.3 - Prob. 2-2SCCh. 3.3 - Prob. 2-3SCCh. 3.3 - Prob. 2-4SCCh. 3.3 - Prob. 2-5SCCh. 3.3 - Prob. 2-6SCCh. 3.3 - Prob. 1SECh. 3.3 - Prob. 2SECh. 3.3 - Prob. 3SECh. 3.3 - Prob. 4SECh. 3.3 - Prob. 5SECh. 3.3 - Prob. 6SECh. 3.3 - Prob. 7SECh. 3.3 - Prob. 8SECh. 3.3 - Prob. 9SECh. 3.3 - Prob. 10SECh. 3.3 - Prob. 11SECh. 3.3 - Prob. 12SECh. 3.3 - Prob. 13SECh. 3.3 - Prob. 14SECh. 3.3 - Prob. 15SECh. 3.3 - Prob. 16SECh. 3.3 - Prob. 17SECh. 3.3 - Prob. 18SECh. 3.3 - Prob. 19SECh. 3.3 - Prob. 20SECh. 3 - Prob. 1ESCh. 3 - Prob. 2ESCh. 3 - Prob. 3ESCh. 3 - Prob. 4ESCh. 3 - Prob. 5ESCh. 3 - Prob. 6ESCh. 3 - Prob. 7ESCh. 3 - Prob. 8ESCh. 3 - Prob. 9ESCh. 3 - Prob. 10ESCh. 3 - Prob. 11ESCh. 3 - Prob. 12ESCh. 3 - Prob. 13ESCh. 3 - Prob. 14ESCh. 3 - Prob. 15ESCh. 3 - Prob. 16ESCh. 3 - Prob. 17ESCh. 3 - Prob. 18ESCh. 3 - Prob. 19ESCh. 3 - Prob. 20ESCh. 3 - Prob. 21ESCh. 3 - Prob. 22ESCh. 3 - Prob. 23ESCh. 3 - Prob. 24ESCh. 3 - Prob. 25ESCh. 3 - Prob. 26ESCh. 3 - Prob. 27ESCh. 3 - Prob. 28ESCh. 3 - Prob. 29ESCh. 3 - Prob. 30ESCh. 3 - Prob. 31ESCh. 3 - Prob. 32ESCh. 3 - Prob. 33ESCh. 3 - Prob. 34ESCh. 3 - Prob. 35ESCh. 3 - Prob. 36ESCh. 3 - Prob. 37ESCh. 3 - Prob. 38ESCh. 3 - Prob. 39ESCh. 3 - Prob. 40ESCh. 3 - Prob. 41ESCh. 3 - Prob. 42ESCh. 3 - Prob. 43ESCh. 3 - Prob. 44ESCh. 3 - Prob. 45ESCh. 3 - Prob. 46ESCh. 3 - Prob. 47ESCh. 3 - Prob. 48ESCh. 3 - Prob. 49ESCh. 3 - Prob. 50ESCh. 3 - Prob. 51ESCh. 3 - Prob. 52ESCh. 3 - Prob. 53ESCh. 3 - Prob. 54ESCh. 3 - Prob. 55ESCh. 3 - Prob. 56ESCh. 3 - Prob. 57ESCh. 3 - Prob. 58ESCh. 3 - Prob. 59ESCh. 3 - Prob. 60ESCh. 3 - Prob. 61ESCh. 3 - Prob. 62ESCh. 3 - Prob. 63ESCh. 3 - Prob. 64ESCh. 3 - Prob. 65ESCh. 3 - Prob. 66ESCh. 3 - Prob. 67ESCh. 3 - Prob. 68ESCh. 3 - Prob. 69ESCh. 3 - Prob. 70ESCh. 3 - Prob. 71ESCh. 3 - Prob. 72ESCh. 3 - Prob. 73ESCh. 3 - Prob. 74ESCh. 3 - Prob. 75ESCh. 3 - Prob. 76ESCh. 3 - Prob. 77ESCh. 3 - Prob. 78ESCh. 3 - Prob. 79ESCh. 3 - Prob. 80ESCh. 3 - Prob. 1PTCh. 3 - Prob. 2PTCh. 3 - Prob. 3PTCh. 3 - Prob. 4PTCh. 3 - Prob. 5PTCh. 3 - Prob. 6PTCh. 3 - Prob. 7PTCh. 3 - Prob. 8PTCh. 3 - Prob. 9PTCh. 3 - Prob. 10PTCh. 3 - Prob. 11PTCh. 3 - Prob. 12PTCh. 3 - Prob. 13PTCh. 3 - Prob. 14PTCh. 3 - Prob. 15PTCh. 3 - Prob. 16PTCh. 3 - Prob. 17PTCh. 3 - Prob. 18PTCh. 3 - Prob. 19PTCh. 3 - Prob. 20PTCh. 3 - Prob. 21PTCh. 3 - Prob. 22PTCh. 3 - Prob. 23PTCh. 3 - Prob. 24PTCh. 3 - Prob. 25PTCh. 3 - Prob. 26PTCh. 3 - Prob. 27PTCh. 3 - Prob. 28PTCh. 3 - Prob. 29PTCh. 3 - Prob. 1CTCh. 3 - Prob. 2CTCh. 3 - Prob. 3CTCh. 3 - Prob. 4CTCh. 3 - Prob. 5CTCh. 3 - Prob. 6CTCh. 3 - Prob. 7CTCh. 3 - Prob. 8CTCh. 3 - Prob. 9CTCh. 3 - Prob. 10CTCh. 3 - Prob. 1CPCh. 3 - Prob. 2CPCh. 3 - Prob. 1CS1Ch. 3 - Prob. 2CS1Ch. 3 - Prob. 3CS1Ch. 3 - Prob. 4CS1Ch. 3 - Prob. 1CS2Ch. 3 - Prob. 2CS2
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- 3) Consider the initial value problem ' y' + 8y = 0, y(0) = -4, y (0) = 16 What is the solution of this initial value problem? A) y = -4t - 2e8t D) y = -4 + 2e-8t B) y = -2 + 2e8t C) y = -2 -2e-8t E) y = -4+ 2e8t F) y = -2t-2e-8tarrow_forward6) Consider the initial value problem y + cos πι + e²бty = 0, y(-1) = 0, y' (-1) = 0 Which of these statements are true? Select all that apply. A) There exists a nonzero real number r such that y(t) = ert is a solution of the initial value problem. B) The constant function y(t) = -1 is a solution of this initial value problem for all real numbers t. C) The constant function y(t) = 0 is the unique solution of this initial value problem on the interval (-∞, ∞). D) This initial value problem has only one solution on the interval (-7, 5). E) There must exist a function y = q(t) that satisfies this initial value problem on the interval (-7,∞).arrow_forward7) Compute the Wronskian of the pair of functions sin(5t) and cos(5t). A) -5 B) 4 C) 1 D) -4 E) 5arrow_forward
- 8) The pair of functions y₁ = eбt and y₁ = teбt forms a fundamental set of solutions for the differential equation y'' - 12y' + 36y= 0.arrow_forward6) Consider the initial value problem y + cos πι + e²бty = 0, y(-1) = 0, y' (-1) = 0 Which of these statements are true? Select all that apply. A) There exists a nonzero real number r such that y(t) = ert is a solution of the initial value problem. B) The constant function y(t) = -1 is a solution of this initial value problem for all real numbers t. C) The constant function y(t) = 0 is the unique solution of this initial value problem on the interval (-∞, ∞). D) This initial value problem has only one solution on the interval (-7, 5). E) There must exist a function y = q(t) that satisfies this initial value problem on the interval (-7,∞).arrow_forward5) Consider the initial value problem 9 (8² 9t+ 1)y' - 8ty = sin(2πt), ) = -4, y = -3.5 16 16 On which of these intervals is this initial value problem certain to have a unique twice differentiable solution? Select all that apply. A) (-∞, ∞) B) (0, 1) 25 C) (-4, -3.5) D) E) 32'32 明arrow_forward
- 1) Which of the following are solutions to the homogeneous second-order differential equation 4y 7y -2y=0? Select all that apply. A) YA = Ce2t, where C is any real constant B) y = 2e-21 6 2t C) y = C (e- 21 + e21), where C is any real constant D) 1/3 = 8 (221 + €21) E) y2 = Ce 2t, where C is any real constant 2t F) y₁ = 8e +2e2t G) y5 = (C₁ e²) · (C₂e-21), where C₁ and C₂ are any real constants 1arrow_forward7) Compute the Wronskian of the pair of functions sin(5t) and cos(5t). A) -5 B) 4 C) 1 D) -4 E) 5arrow_forward5) Consider the initial value problem 9 (8² 9t+ 1)y' - 8ty = sin(2πt), ) = -4, y = -3.5 16 16 On which of these intervals is this initial value problem certain to have a unique twice differentiable solution? Select all that apply. A) (-∞, ∞) B) (0, 1) 25 C) (-4, -3.5) D) E) 32'32 明arrow_forward
- 2) For which of these differential equations is the characteristic equation given by r(10r + 1) = 0? A) y (10y + 1) = 0 B) 10y'' + 1 = 0 C) 10y+1y=0 D) y (10y + 1y) = 0 E) 10y'' + 1y=0arrow_forwardS 36. lim 5x+2 x-2 37. lim √√2x4 + x² x-3 Answer-> 2x3 +4 38. lim x12 √ x² + 1 √√x² + 8 39. lim x-1 2x+4 Answer 40. lim x3 2x x√x² + 7 √√2x+3arrow_forwardSee imagearrow_forward
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