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Math
CalculusCalculus (MindTap Course List)11th Edition

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Chapter 5.8, Problem 55E
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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Slope Field In Exercises 55 and 56, a differential equation, a point, and a slope field are given, (a) Sketch two approximate solutions of the differential equation on the slope field, one of which passes through the given point. (To print an enlarged copy of the graph, go to MathGraphs.com.) (b) Use integration and the given point to find the particular solution of the differential equation and use a graphing utility to graph the solution. Compare the result with the sketch in part (a) that passes through the given point.

d y d x = 2 9 + x 2 ,       ( 0 , 2 )

images

(a)

To determine

To graph: The stated differentialequation’s dydx=29+x2 two approximate solutions on slope field.

Explanation

Given:

The differential equation, slope field and a point are stated.

dydx=29+x2, (0,2)

Graph:

Observe the stateddifferential equation:

dydx=29+x2

Implement Euler’s method to discover the approximate solution. Implement a step size,

h=0.5, x0=0, y0=2 and F(x,y)=29+x2

Evaluate the approximate values of y,

For x = 0 and y = 2

y1=y0+hF(x0,y0)y1=2+0.5(29+(0)2)y1=2.1111

For x = 0.5 and y = 2.1111

y2=y1+hF(x1,y1)y2=2.1111+0.5(29+(0.5)2)y2=2.2192

For x = 1 and y = 2.2192

y3=y2+hF(x2,y2)y3=2.2192+0.5(29+(1)2)y3=2.3192

For x = 1.5 and y = 2.3192

y4=y3+hF(x3,y3)y4=2.3192+0.5(29+(1.5)2)y4=2.4080

For x = 2 and y = 2.4080

y5=y4+hF(x4,y4)y5=2.408+0.5(29+(2)2)y5=2.4849

For x = 2.5 and y = 2.4849

y6=y5+hF(x5,y5)y6=2.4849+0.5(29+(2.5)2)y6=2.5504

For x = 3and y = 2.5504

y7=y6+hF(x6,y6)y7=2.5504+0.5(29+(3)2)y7=2.6059

For x = 3.5 and y = 2.6059

y8=y7+hF(x7,y7)y8=2.6059+0.5(29+(3.5)2)y8=2.6530

The point coordinates acquired are shown in the following table:

xn yn=yn−1+hF(xn−1,yn−1) Points (xn,yn)
0 2 (0, 2)
0.5 2.1111 (0

(b)

To determine

To graph: The exactsolution of stateddifferential equation dydx=29+x2.

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Chapter 5.8,
Problem 54E
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Problem 56E
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P-28ESect-5.7 P-29ESect-5.7 P-30ESect-5.7 P-31ESect-5.7 P-32ESect-5.7 P-33ESect-5.7 P-34ESect-5.7 P-35ESect-5.7 P-36ESect-5.7 P-37ESect-5.7 P-38ESect-5.7 P-39ESect-5.7 P-40ESect-5.7 P-41ESect-5.7 P-42ESect-5.7 P-43ESect-5.7 P-44ESect-5.7 P-45ESect-5.7 P-46ESect-5.7 P-47ESect-5.7 P-48ESect-5.7 P-49ESect-5.7 P-50ESect-5.7 P-51ESect-5.7 P-52ESect-5.7 P-53ESect-5.7 P-54ESect-5.7 P-55ESect-5.7 P-56ESect-5.7 P-57ESect-5.7 P-58ESect-5.7 P-59ESect-5.7 P-60ESect-5.7 P-61ESect-5.7 P-62ESect-5.7 P-63ESect-5.7 P-64ESect-5.7 P-65ESect-5.7 P-66ESect-5.7 P-67ESect-5.7 P-68ESect-5.7 P-69ESect-5.7 P-70ESect-5.7 P-71ESect-5.7 P-72ESect-5.7 P-73ESect-5.7 P-74ESect-5.7 P-75ESect-5.7 P-76ESect-5.7 P-77ESect-5.7 P-78ESect-5.7 P-79ESect-5.7 P-80ESect-5.7 P-81ESect-5.7 P-82ESect-5.7 P-83ESect-5.7 P-84ESect-5.7 P-85ESect-5.7 P-86ESect-5.7 P-87ESect-5.7 P-88ESect-5.7 P-89ESect-5.7 P-90ESect-5.7 P-91ESect-5.7 P-92ESect-5.7 P-93ESect-5.7 P-94ESect-5.7 P-95ESect-5.7 P-96ESect-5.7 P-97ESect-5.7 P-98ESect-5.7 P-99ESect-5.7 P-100ESect-5.8 P-1ESect-5.8 P-2ESect-5.8 P-3ESect-5.8 P-4ESect-5.8 P-5ESect-5.8 P-6ESect-5.8 P-7ESect-5.8 P-8ESect-5.8 P-9ESect-5.8 P-10ESect-5.8 P-11ESect-5.8 P-12ESect-5.8 P-13ESect-5.8 P-14ESect-5.8 P-15ESect-5.8 P-16ESect-5.8 P-17ESect-5.8 P-18ESect-5.8 P-19ESect-5.8 P-20ESect-5.8 P-21ESect-5.8 P-22ESect-5.8 P-23ESect-5.8 P-24ESect-5.8 P-25ESect-5.8 P-26ESect-5.8 P-27ESect-5.8 P-28ESect-5.8 P-29ESect-5.8 P-30ESect-5.8 P-31ESect-5.8 P-32ESect-5.8 P-33ESect-5.8 P-34ESect-5.8 P-35ESect-5.8 P-36ESect-5.8 P-37ESect-5.8 P-38ESect-5.8 P-39ESect-5.8 P-40ESect-5.8 P-41ESect-5.8 P-42ESect-5.8 P-43ESect-5.8 P-44ESect-5.8 P-45ESect-5.8 P-46ESect-5.8 P-47ESect-5.8 P-48ESect-5.8 P-49ESect-5.8 P-50ESect-5.8 P-51ESect-5.8 P-52ESect-5.8 P-53ESect-5.8 P-54ESect-5.8 P-55ESect-5.8 P-56ESect-5.8 P-57ESect-5.8 P-58ESect-5.8 P-59ESect-5.8 P-60ESect-5.8 P-61ESect-5.8 P-62ESect-5.8 P-63ESect-5.8 P-64ESect-5.8 P-65ESect-5.8 P-66ESect-5.8 P-67ESect-5.8 P-68ESect-5.8 P-69ESect-5.8 P-70ESect-5.8 P-71ESect-5.8 P-72ESect-5.8 P-73ESect-5.8 P-74ESect-5.8 P-75ESect-5.8 P-76ESect-5.8 P-77ESect-5.8 P-78ESect-5.9 P-1ESect-5.9 P-2ESect-5.9 P-3ESect-5.9 P-4ESect-5.9 P-5ESect-5.9 P-6ESect-5.9 P-7ESect-5.9 P-8ESect-5.9 P-9ESect-5.9 P-10ESect-5.9 P-11ESect-5.9 P-12ESect-5.9 P-13ESect-5.9 P-14ESect-5.9 P-15ESect-5.9 P-16ESect-5.9 P-17ESect-5.9 P-18ESect-5.9 P-19ESect-5.9 P-20ESect-5.9 P-21ESect-5.9 P-22ESect-5.9 P-23ESect-5.9 P-24ESect-5.9 P-25ESect-5.9 P-26ESect-5.9 P-27ESect-5.9 P-28ESect-5.9 P-29ESect-5.9 P-30ESect-5.9 P-31ESect-5.9 P-32ESect-5.9 P-33ESect-5.9 P-34ESect-5.9 P-35ESect-5.9 P-36ESect-5.9 P-37ESect-5.9 P-38ESect-5.9 P-39ESect-5.9 P-40ESect-5.9 P-41ESect-5.9 P-42ESect-5.9 P-43ESect-5.9 P-44ESect-5.9 P-45ESect-5.9 P-46ESect-5.9 P-47ESect-5.9 P-48ESect-5.9 P-49ESect-5.9 P-50ESect-5.9 P-51ESect-5.9 P-52ESect-5.9 P-53ESect-5.9 P-54ESect-5.9 P-55ESect-5.9 P-56ESect-5.9 P-57ESect-5.9 P-58ESect-5.9 P-59ESect-5.9 P-60ESect-5.9 P-61ESect-5.9 P-62ESect-5.9 P-63ESect-5.9 P-64ESect-5.9 P-65ESect-5.9 P-66ESect-5.9 P-67ESect-5.9 P-68ESect-5.9 P-69ESect-5.9 P-70ESect-5.9 P-71ESect-5.9 P-72ESect-5.9 P-73ESect-5.9 P-74ESect-5.9 P-75ESect-5.9 P-76ESect-5.9 P-77ESect-5.9 P-78ESect-5.9 P-79ESect-5.9 P-80ESect-5.9 P-81ESect-5.9 P-82ESect-5.9 P-83ESect-5.9 P-84ESect-5.9 P-85ESect-5.9 P-86ESect-5.9 P-87ESect-5.9 P-88ESect-5.9 P-89ESect-5.9 P-90ESect-5.9 P-91ESect-5.9 P-92ESect-5.9 P-93ESect-5.9 P-94ESect-5.9 P-95ESect-5.9 P-96ESect-5.9 P-97ESect-5.9 P-98ESect-5.9 P-99ESect-5.9 P-100ESect-5.9 P-101ESect-5.9 P-102ESect-5.9 P-103ESect-5.9 P-104ESect-5.9 P-105ESect-5.9 P-106ECh-5 P-1RECh-5 P-2RECh-5 P-3RECh-5 P-4RECh-5 P-5RECh-5 P-6RECh-5 P-7RECh-5 P-8RECh-5 P-9RECh-5 P-10RECh-5 P-11RECh-5 P-12RECh-5 P-13RECh-5 P-14RECh-5 P-15RECh-5 P-16RECh-5 P-17RECh-5 P-18RECh-5 P-19RECh-5 P-20RECh-5 P-21RECh-5 P-22RECh-5 P-23RECh-5 P-24RECh-5 P-25RECh-5 P-26RECh-5 P-27RECh-5 P-28RECh-5 P-29RECh-5 P-30RECh-5 P-31RECh-5 P-32RECh-5 P-33RECh-5 P-34RECh-5 P-35RECh-5 P-36RECh-5 P-37RECh-5 P-38RECh-5 P-39RECh-5 P-40RECh-5 P-41RECh-5 P-42RECh-5 P-43RECh-5 P-44RECh-5 P-45RECh-5 P-46RECh-5 P-47RECh-5 P-48RECh-5 P-49RECh-5 P-50RECh-5 P-51RECh-5 P-52RECh-5 P-53RECh-5 P-54RECh-5 P-55RECh-5 P-56RECh-5 P-57RECh-5 P-58RECh-5 P-59RECh-5 P-60RECh-5 P-61RECh-5 P-62RECh-5 P-63RECh-5 P-64RECh-5 P-65RECh-5 P-66RECh-5 P-67RECh-5 P-68RECh-5 P-69RECh-5 P-70RECh-5 P-71RECh-5 P-72RECh-5 P-73RECh-5 P-74RECh-5 P-75RECh-5 P-76RECh-5 P-77RECh-5 P-78RECh-5 P-79RECh-5 P-80RECh-5 P-81RECh-5 P-82RECh-5 P-83RECh-5 P-84RECh-5 P-85RECh-5 P-86RECh-5 P-87RECh-5 P-88RECh-5 P-89RECh-5 P-90RECh-5 P-91RECh-5 P-92RECh-5 P-93RECh-5 P-94RECh-5 P-95RECh-5 P-96RECh-5 P-97RECh-5 P-98RECh-5 P-99RECh-5 P-100RECh-5 P-101RECh-5 P-102RECh-5 P-103RECh-5 P-104RECh-5 P-105RECh-5 P-106RECh-5 P-107RECh-5 P-108RECh-5 P-109RECh-5 P-110RECh-5 P-111RECh-5 P-112RECh-5 P-113RECh-5 P-114RECh-5 P-115RECh-5 P-116RECh-5 P-117RECh-5 P-118RECh-5 P-119RECh-5 P-120RECh-5 P-121RECh-5 P-122RECh-5 P-123RECh-5 P-124RECh-5 P-125RECh-5 P-126RECh-5 P-127RECh-5 P-128RECh-5 P-129RECh-5 P-130RECh-5 P-131RECh-5 P-132RECh-5 P-133RECh-5 P-134RECh-5 P-1PSCh-5 P-2PSCh-5 P-3PSCh-5 P-4PSCh-5 P-5PSCh-5 P-6PSCh-5 P-7PSCh-5 P-8PSCh-5 P-9PSCh-5 P-10PSCh-5 P-11PSCh-5 P-12PSCh-5 P-13PSCh-5 P-14PSCh-5 P-15PSCh-5 P-16PSCh-5 P-17PS

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