Explanation Given Information: The provided differential equation is ( x + 1 ) y ' + y = 0 and its general solution is y = c x + 1 . Also, the given values of c are 0 , ± 1 , ± 2 . Graph: Consider the general solution y = c x + 1 of the differential equation ( x + 1 ) y ' + y = 0 . Now, substitute c = 0 , c = ± 1 , c = ± 2 one by one to get particular solutions of the provided differential equation and draw their graph. If c = 0 , y = c x + 1 = 0 x + 1 = 0 Choose some values for x and compute the value for y , in order to form the ordered pairs. Put x = 0 in the function y = 0 . Then, y = 0 Put x = 1 in the function y = 0 . Then, y = 0 Put x = 2 in the function y = 0 . Then, y = 0 The required table is shown below, x y ( x , y ) 0 0 ( 0 , 0 ) 1 0 ( 1 , 0 ) 2 0 ( 2 , 0 ) Plot these ordered pairs on the graph and join them with a straight line. Therefore, the graph of the function y = 0 is, If c = 1 , y = c x + 1 = 1 x + 1 The above function is not defined on x = − 1 . So, the graph of y = 1 x + 1 has an asymptote at x = − 1 . Choose some values for x and compute the value for y , in order to form the ordered pairs. Put x = 0 in the function y = 1 x + 1 . Then, y = 1 0 + 1 = 1 Put x = 1 in the function y = 1 x + 1 . Then, y = 1 1 + 1 = 1 2 = 0.5 Put x = 3 in the function y = 1 x + 1 . Then, y = 1 3 + 1 = 1 4 = 0.25 Put x = − 2 in the function y = 1 x + 1 . Then, y = 1 − 2 + 1 = 1 − 1 = − 1 Put x = − 3 in the function y = 1 x + 1 . Then, y = 1 − 3 + 1 = 1 − 2 = − 0.5 Put x = − 5 in the function y = 1 x + 1 . Then, y = 1 − 5 + 1 = 1 − 4 = − 0.25 The required table is shown below, x y ( x , y ) 0 1 ( 0 , 1 ) 1 0.5 ( 1 , 0.5 ) 3 0.25 ( 3 , 0.25 ) − 2 − 1 ( − 2 , − 1 ) − 3 − 0.5 ( − 3 , − 0.5 ) − 5 − 0.25 ( − 5 , − 0.25 ) Now, find the limit of the function y = 1 x + 1 when x → ∞ . lim x → ∞ y = lim x → ∞ 1 x + 1 → 0 So, as x → ∞ , y → 0 . Find the right hand limit of the function y = 1 x + 1 at x = − 1 . lim x → − 1 + y = lim x → − 1 + 1 x + 1 Put x = − 1 + h where h → 0 . Then, lim x → − 1 + y = lim x → − 1 + 1 x + 1 = lim h → 0 1 − 1 + h + 1 = lim h → 0 1 h → ∞ So, as x → − 1 from right, y → ∞ . Find left-hand limit of the function y = 1 x + 1 at x = − 1 . lim x → − 1 − y = lim x → − 1 − 1 x + 1 Put x = − 1 − h where h → 0 . Then, lim x → − 1 − y = lim x → − 1 − 1 x + 1 = lim h → 0 1 − 1 − h + 1 = lim h → 0 − 1 h → − ∞ So, as x → − 1 from left, y → − ∞ . Now, find the limit of the function y = 1 x + 1 when x → − ∞ . lim x → − ∞ y = lim x → − ∞ 1 x + 1 → 0 So, as x → − ∞ , y → 0 . Plot the ordered pairs on the graph and join them with a free hand. Therefore, the graph of the function y = 1 x + 1 is, If c = − 1 , y = c x + 1 = − 1 x + 1 The above function is not defined on x = − 1 . So, the graph of y = − 1 x + 1 has an asymptote at x = − 1 . Choose some values for x and compute the value for y , in order to form the ordered pairs. Put x = − 5 in the function y = − 1 x + 1 . Then, y = − 1 − 5 + 1 = − 1 − 4 = 0.25 Put x = − 3 in the function y = − 1 x + 1 . Then, y = − 1 − 3 + 1 = − 1 − 2 = 0.5 Put x = − 2 in the function y = − 1 x + 1 . Then, y = − 1 − 2 + 1 = − 1 − 1 = 1 Put x = 0 in the function y = − 1 x + 1 . Then, y = − 1 0 + 1 = − 1 1 = − 1 Put x = 1 in the function y = − 1 x + 1 . Then, y = − 1 1 + 1 = − 1 2 = − 0.5 Put x = 3 in the function y = − 1 x + 1 . Then, y = − 1 3 + 1 = − 1 4 = − 0.25 The required table is shown below, x y ( x , y ) − 5 0.25 ( − 5 , 0.25 ) − 3 0.5 ( − 3 , 0.5 ) − 2 1 ( − 2 , 1 ) 0 − 1 ( 0 , − 1 ) 1 − 0.5 ( 1 , − 0.5 ) 3 − 0.25 ( 3 , − 0.25 ) Now, find the limit of the function y = − 1 x + 1 when x → ∞ . lim x → ∞ y = lim x → ∞ − 1 x + 1 → 0 So, as x → ∞ , y → 0 . Find the right hand limit of the function y = − 1 x + 1 at x = − 1 . lim x → − 1 + y = lim x → − 1 + − 1 x + 1 Put x = − 1 + h where h → 0 . Then, lim x → − 1 + y = lim x → − 1 + − 1 x + 1 = lim h → 0 − 1 − 1 + h + 1 = lim h → 0 − 1 h → − ∞ So, as x → − 1 from right, y → − ∞ . Find left-hand limit of the function y = − 1 x + 1 at x = − 1 . lim x → − 1 − y = lim x → − 1 − − 1 x + 1 Put x = − 1 − h where h → 0 . Then, lim x → − 1 − y = lim x → − 1 − − 1 x + 1 = lim h → 0 − 1 − 1 − h + 1 = lim h → 0 1 h → ∞ So, as x → − 1 from left, y → ∞

WebAssign Printed Access Card for Larson's Calculus: An Applied Approach, 10th Edition, Single-Term

10th Edition

ISBN: 9781337652308

Author: Ron Larson

Publisher: Brooks Cole

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Chapter 11, Problem 20RE

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To graph: The particular solutions y=cx+1 where c=0, c=±1, c=±2 of the differential equation (x+1)y'+y=0.

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Chapter 11, Problem 19RE

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Chapter 11 Solutions

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Ch. 11.1 - Checkpoint 1 Worked-out solution available at...Ch. 11.1 - Prob. 2CP Ch. 11.1 - Prob. 3CP Ch. 11.1 - Prob. 4CP Ch. 11.1 - Prob. 1SWU Ch. 11.1 - Prob. 2SWU Ch. 11.1 - Prob. 3SWU Ch. 11.1 - Prob. 4SWU Ch. 11.1 - Prob. 5SWU Ch. 11.1 - Prob. 6SWU

Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Verifying Solutions In Exercises 1-12, verify the...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Determining Solutions In Exercises 1316, determine...Ch. 11.1 - Prob. 16E Ch. 11.1 - Determining Solutions In Exercises 1720, determine...Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Prob. 35E Ch. 11.1 - Prob. 36E Ch. 11.1 - Prob. 37E Ch. 11.1 - Prob. 38E Ch. 11.1 - Prob. 39E Ch. 11.1 - Investment The rate of growth of an investment is...Ch. 11.1 - Prob. 41E Ch. 11.1 - Prob. 42E Ch. 11.1 - Prob. 43E Ch. 11.1 - Prob. 44E Ch. 11.1 - Prob. 45E Ch. 11.1 - Prob. 46E Ch. 11.2 - Checkpoint 1 Worked-out solution available at...Ch. 11.2 - Prob. 2CP Ch. 11.2 - Prob. 3CP Ch. 11.2 - Prob. 4CP Ch. 11.2 - Prob. 5CP Ch. 11.2 - Prob. 6CP Ch. 11.2 - Prob. 1SWU Ch. 11.2 - Prob. 2SWU Ch. 11.2 - Prob. 3SWU Ch. 11.2 - Prob. 4SWU Ch. 11.2 - Prob. 5SWU Ch. 11.2 - Prob. 6SWU Ch. 11.2 - Prob. 7SWU Ch. 11.2 - Prob. 8SWU Ch. 11.2 - Prob. 9SWU Ch. 11.2 - Prob. 10SWU Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E Ch. 11.2 - Prob. 7E Ch. 11.2 - Prob. 8E Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - Prob. 12E Ch. 11.2 - Prob. 13E Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - Prob. 18E Ch. 11.2 - Prob. 19E Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - Prob. 29E Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 33E Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 35E Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 37E Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E Ch. 11.2 - Prob. 41E Ch. 11.2 - Prob. 42E Ch. 11.2 - Prob. 43E Ch. 11.2 - Prob. 44E Ch. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Solve the differential equation. Weight Gain A...Ch. 11.2 - Prob. 1QY Ch. 11.2 - Prob. 2QY Ch. 11.2 - Prob. 3QY Ch. 11.2 - Prob. 4QY Ch. 11.2 - Prob. 5QY Ch. 11.2 - Prob. 6QY Ch. 11.2 - Prob. 7QY Ch. 11.2 - Prob. 8QY Ch. 11.2 - Prob. 9QY Ch. 11.2 - Prob. 10QY Ch. 11.2 - Prob. 11QY Ch. 11.2 - Prob. 12QY Ch. 11.2 - Prob. 13QY Ch. 11.2 - Prob. 14QY Ch. 11.2 - Prob. 15QY Ch. 11.2 - Ignoring resistance, a sailboat starting from rest...Ch. 11.3 - Checkpoint 1 Worked-out solution available at...Ch. 11.3 - Prob. 2CP Ch. 11.3 - Prob. 3CP Ch. 11.3 - Prob. 1SWU Ch. 11.3 - Prob. 2SWU Ch. 11.3 - Prob. 3SWU Ch. 11.3 - Prob. 4SWU Ch. 11.3 - Prob. 5SWU Ch. 11.3 - Prob. 6SWU Ch. 11.3 - Prob. 7SWU Ch. 11.3 - Prob. 8SWU Ch. 11.3 - In Exercises 5-10, find the indefinite integral....Ch. 11.3 - Prob. 10SWU Ch. 11.3 - Prob. 1E Ch. 11.3 - Prob. 2E Ch. 11.3 - Prob. 3E Ch. 11.3 - Prob. 4E Ch. 11.3 - Prob. 5E Ch. 11.3 - Prob. 6E Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 10E Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 13E Ch. 11.3 - Prob. 14E Ch. 11.3 - Prob. 15E Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 17E Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Using Two Methods In Exercises 19-22, solve for y...Ch. 11.3 - Prob. 20E Ch. 11.3 - Prob. 21E Ch. 11.3 - Prob. 22E Ch. 11.3 - Prob. 23E Ch. 11.3 - Prob. 24E Ch. 11.3 - Prob. 25E Ch. 11.3 - Prob. 26E Ch. 11.3 - Prob. 27E Ch. 11.3 - Prob. 28E Ch. 11.3 - Prob. 29E Ch. 11.3 - Prob. 30E Ch. 11.3 - Prob. 31E Ch. 11.3 - Prob. 32E Ch. 11.3 - Finding a Particular Solution In Exercises 27-34,...Ch. 11.3 - Prob. 34E Ch. 11.3 - Prob. 35E Ch. 11.3 - Prob. 36E Ch. 11.3 - Vertical Motion A falling object encounters air...Ch. 11.3 - Velocity A booster rocket carrying an observation...Ch. 11.3 - Learning Curve The management at a medical supply...Ch. 11.3 - Investment Let A he the amount in a fund earning...Ch. 11.4 - Prob. 1CP Ch. 11.4 - Prob. 2CP Ch. 11.4 - Checkpoint 3 Worked-out solution available at...Ch. 11.4 - Prob. 4CP Ch. 11.4 - Checkpoint 5 Worked-out solution available at...Ch. 11.4 - Prob. 1SWU Ch. 11.4 - Prob. 2SWU Ch. 11.4 - Prob. 3SWU Ch. 11.4 - Prob. 4SWU Ch. 11.4 - Prob. 5SWU Ch. 11.4 - Prob. 6SWU Ch. 11.4 - Prob. 7SWU Ch. 11.4 - Prob. 8SWU Ch. 11.4 - Prob. 9SWU Ch. 11.4 - Prob. 10SWU Ch. 11.4 - Prob. 1E Ch. 11.4 - Prob. 2E Ch. 11.4 - Advertising Awareness In Exercises 3 and 4, use...Ch. 11.4 - Prob. 4E Ch. 11.4 - Prob. 5E Ch. 11.4 - Prob. 6E Ch. 11.4 - Prob. 7E Ch. 11.4 - Prob. 8E Ch. 11.4 - Prob. 9E Ch. 11.4 - Prob. 10E Ch. 11.4 - Prob. 11E Ch. 11.4 - Prob. 12E Ch. 11.4 - Prob. 13E Ch. 11.4 - Prob. 14E Ch. 11.4 - Prob. 15E Ch. 11.4 - Prob. 16E Ch. 11.4 - Prob. 17E Ch. 11.4 - Chemistry A wet towel hung from a clothesline to...Ch. 11.4 - Prob. 19E Ch. 11.4 - Prob. 20E Ch. 11.4 - Biology A population of eight beavers has been...Ch. 11.4 - Prob. 22E Ch. 11.4 - Prob. 23E Ch. 11.4 - Prob. 24E Ch. 11.4 - Chemical Mixture A 100-gallon tank is full of a...Ch. 11.4 - Chemical Mixture A 200-gallon tank is half full of...Ch. 11.4 - Prob. 29E Ch. 11.4 - Prob. 30E Ch. 11.4 - Prob. 31E Ch. 11.4 - Prob. 32E Ch. 11.4 - Prob. 33E Ch. 11.4 - Prob. 34E Ch. 11.4 - Prob. 35E Ch. 11.4 - Prob. 36E Ch. 11.4 - Prob. 37E Ch. 11.4 - Prob. 38E Ch. 11 - Prob. 1RE Ch. 11 - Prob. 2RE Ch. 11 - Prob. 3RE Ch. 11 - Prob. 4RE Ch. 11 - Prob. 5RE Ch. 11 - Prob. 6RE Ch. 11 - Prob. 7RE Ch. 11 - Prob. 8RE Ch. 11 - Prob. 9RE Ch. 11 - Prob. 10RE Ch. 11 - Prob. 11RE Ch. 11 - Prob. 12RE Ch. 11 - Prob. 13RE Ch. 11 - Prob. 14RE Ch. 11 - Finding a Particular Solution In Exercises 15 and...Ch. 11 - Prob. 16RE Ch. 11 - Prob. 17RE Ch. 11 - Prob. 18RE Ch. 11 - Prob. 19RE Ch. 11 - Prob. 20RE Ch. 11 - Prob. 21RE Ch. 11 - Prob. 22RE Ch. 11 - Prob. 23RE Ch. 11 - Prob. 24RE Ch. 11 - Prob. 25RE Ch. 11 - Prob. 26RE Ch. 11 - Prob. 27RE Ch. 11 - Prob. 28RE Ch. 11 - Prob. 29RE Ch. 11 - Prob. 30RE Ch. 11 - Prob. 31RE Ch. 11 - Prob. 32RE Ch. 11 - Prob. 33RE Ch. 11 - Prob. 34RE Ch. 11 - Prob. 35RE Ch. 11 - Prob. 36RE Ch. 11 - Prob. 37RE Ch. 11 - Prob. 38RE Ch. 11 - Prob. 39RE Ch. 11 - Prob. 40RE Ch. 11 - Prob. 41RE Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Prob. 43RE Ch. 11 - Prob. 44RE Ch. 11 - Prob. 45RE Ch. 11 - Prob. 46RE Ch. 11 - Prob. 47RE Ch. 11 - Prob. 48RE Ch. 11 - Prob. 49RE Ch. 11 - Prob. 50RE Ch. 11 - Prob. 51RE Ch. 11 - Prob. 52RE Ch. 11 - Prob. 53RE Ch. 11 - Prob. 54RE Ch. 11 - Prob. 55RE Ch. 11 - Prob. 56RE Ch. 11 - Solving a Linear Differential Equation In...Ch. 11 - Prob. 58RE Ch. 11 - Prob. 59RE Ch. 11 - Prob. 60RE Ch. 11 - Prob. 61RE Ch. 11 - Prob. 62RE Ch. 11 - Prob. 63RE Ch. 11 - Prob. 64RE Ch. 11 - Prob. 65RE Ch. 11 - Prob. 66RE Ch. 11 - Safety Assume the rate of change per hour in the...Ch. 11 - Prob. 68RE Ch. 11 - Prob. 69RE Ch. 11 - Prob. 70RE Ch. 11 - Prob. 71RE Ch. 11 - Prob. 72RE Ch. 11 - Prob. 73RE Ch. 11 - Prob. 74RE Ch. 11 - Prob. 75RE Ch. 11 - Chemical Mixture A tank contains 30 gallons of a...Ch. 11 - Chemical Mixture A tank contains 20 gallons of a...Ch. 11 - Prob. 1TYS Ch. 11 - Prob. 2TYS Ch. 11 - Prob. 3TYS Ch. 11 - Prob. 4TYS Ch. 11 - Prob. 5TYS Ch. 11 - Prob. 6TYS Ch. 11 - Prob. 7TYS Ch. 11 - Prob. 8TYS Ch. 11 - Prob. 9TYS Ch. 11 - Prob. 10TYS Ch. 11 - Prob. 11TYS Ch. 11 - A lamb that weighs 10 pounds at birth gains weight...Ch. 11 - Prob. 13TYS

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To graph: The particular solutions y = c x + 1 where c = 0 , c = ± 1 , c = ± 2 of the differential equation ( x + 1 ) y ' + y = 0 .

Solution Summary: The author explains how to graph the particular solutions of the differential equation (x+1)y'+y=0.

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To graph: The particular solutions y=cx+1 where c=0, c=±1, c=±2 of the differential equation (x+1)y'+y=0.

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Chapter 11 Solutions