Explanation The approximations to the solution of the initial-value problem d y d x = F ( x , y ) with the initial condition y ( x 0 ) = y 0 can be computed as follows. Note that, Euler’s method assumes the solution written in the Taylor’s series form. That is, the function is of the form, y ( x + h ) ≈ y ( x ) + h y ′ ( x ) + h 2 y ″ ( x ) 2 ! + h 3 y ‴ ( x ) 3 ! + ... . The above approximation is reasonable when plenty of terms were taken, and if the value of h is reasonably small. But for Euler’s method only first two terms will be considered. That is, y ( x + h ) ≈ y ( x ) + h y ′ ( x ) (1) Here, the last term is h times of d y d x . So, the equation (1) can be rewritten as y ( x + h ) ≈ y ( x ) + h f ( x , y ) . The value of y 1 can be computed as follows. Let y be the known value which can be represent as y 0 . It has this value while x = x 0 . That is, the initial value is ( x 0 , y 0 )

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Chapter 9.4, Problem 1CQ

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To describe: The ideas behind the Euler’s method for finding the approximations to the solution of the initial-value problem dydx=F(x,y) with the initial condition y(x0)=y0.

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Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 9.1 - Prob. 1CQ Ch. 9.1 - Prob. 2CQ Ch. 9.1 - Prob. 3CQ Ch. 9.1 - Prob. 4CQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E

Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - SUPPLY AND DEMAND Let S(t) denote the supply of a...Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - AMOUNT OF GLUCOSE IN THE BLOODSTREAM Suppose...Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - GOMPERTZ GROWTH CURVE Suppose a quantity Q(t) does...Ch. 9.1 - Prob. 29E Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.2 - Prob. 1CQ Ch. 9.2 - Prob. 2CQ Ch. 9.2 - Prob. 3CQ Ch. 9.2 - Prob. 1E Ch. 9.2 - Prob. 2E Ch. 9.2 - In Exercises 116, solve the first-order...Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - Prob. 13E Ch. 9.2 - Prob. 14E Ch. 9.2 - Prob. 15E Ch. 9.2 - Prob. 16E Ch. 9.2 - Prob. 17E Ch. 9.2 - Prob. 18E Ch. 9.2 - Prob. 19E Ch. 9.2 - Prob. 20E Ch. 9.2 - Prob. 21E Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Prob. 30E Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.2 - Prob. 33E Ch. 9.2 - Prob. 34E Ch. 9.2 - Prob. 35E Ch. 9.2 - Prob. 36E Ch. 9.2 - Prob. 37E Ch. 9.2 - Prob. 38E Ch. 9.2 - Prob. 39E Ch. 9.2 - Prob. 40E Ch. 9.2 - Prob. 41E Ch. 9.2 - Prob. 42E Ch. 9.3 - Prob. 1CQ Ch. 9.3 - Prob. 2CQ Ch. 9.3 - Prob. 1E Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - NEWTONS LAW OF COOLING Newtons Law of Cooling...Ch. 9.3 - Prob. 9E Ch. 9.3 - EXPONENTAL DECAY A radioactive isotope with an...Ch. 9.3 - RADIOACTIVE DECAY If 4 g of a radioactive...Ch. 9.3 - LEARNING CURVES The American Court Reporter...Ch. 9.3 - Prob. 13E Ch. 9.3 - Prob. 14E Ch. 9.3 - Prob. 15E Ch. 9.3 - Prob. 16E Ch. 9.3 - Prob. 17E Ch. 9.3 - SINKING FUNDS The proprietor of Carson Hardware...Ch. 9.3 - Prob. 19E Ch. 9.3 - GROWTH OF A FRUIT FLY COLONY A biologist has...Ch. 9.3 - Prob. 21E Ch. 9.3 - Prob. 22E Ch. 9.3 - Prob. 23E Ch. 9.3 - Prob. 25E Ch. 9.3 - Prob. 26E Ch. 9.3 - Prob. 27E Ch. 9.3 - Prob. 28E Ch. 9.3 - Von Bertalanffy Growth Model The von Bertalanffy...Ch. 9.3 - Prob. 30E Ch. 9.3 - Prob. 31E Ch. 9.3 - MIXTURE PROBLEMS A tank initially contains 50 gal...Ch. 9.4 - Prob. 1CQ Ch. 9.4 - Prob. 2CQ Ch. 9.4 - Prob. 1E Ch. 9.4 - Prob. 2E Ch. 9.4 - Prob. 3E Ch. 9.4 - Prob. 4E Ch. 9.4 - Prob. 5E Ch. 9.4 - Prob. 6E Ch. 9.4 - Prob. 7E Ch. 9.4 - Prob. 8E Ch. 9.4 - Prob. 9E Ch. 9.4 - Prob. 10E Ch. 9.4 - Prob. 11E Ch. 9.4 - Prob. 12E Ch. 9.4 - Prob. 13E Ch. 9.4 - Prob. 14E Ch. 9.4 - Prob. 15E Ch. 9.4 - Prob. 16E Ch. 9 - Prob. 1CRQ Ch. 9 - Prob. 2CRQ Ch. 9 - Prob. 3CRQ Ch. 9 - Prob. 4CRQ Ch. 9 - Prob. 5CRQ Ch. 9 - Prob. 1RE Ch. 9 - Prob. 2RE Ch. 9 - Prob. 3RE Ch. 9 - Prob. 4RE Ch. 9 - Prob. 5RE Ch. 9 - Prob. 6RE Ch. 9 - Prob. 7RE Ch. 9 - Prob. 8RE Ch. 9 - Prob. 9RE Ch. 9 - Prob. 10RE Ch. 9 - Prob. 11RE Ch. 9 - Prob. 12RE Ch. 9 - Prob. 13RE Ch. 9 - Prob. 14RE Ch. 9 - Prob. 15RE Ch. 9 - Prob. 16RE Ch. 9 - Prob. 17RE Ch. 9 - Prob. 18RE Ch. 9 - RESALE VALUE OF A MACHINE The resale value of a...Ch. 9 - Prob. 20RE Ch. 9 - Prob. 21RE Ch. 9 - Prob. 22RE Ch. 9 - Prob. 23RE Ch. 9 - Prob. 24RE Ch. 9 - Prob. 25RE Ch. 9 - Prob. 26RE Ch. 9 - Prob. 27RE Ch. 9 - Prob. 28RE Ch. 9 - Prob. 1BM Ch. 9 - Prob. 2BM Ch. 9 - Prob. 3BM Ch. 9 - Prob. 4BM

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The ideas behind the Euler’s method for finding the approximations to the solution of the initial-value problem d y d x = F ( x , y ) with the initial condition y ( x 0 ) = y 0 .

Solution Summary: The author describes Euler's method for finding the approximations to the solution of the initial-value problem.

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To describe: The ideas behind the Euler’s method for finding the approximations to the solution of the initial-value problem dydx=F(x,y) with the initial condition y(x0)=y0.

Chapter 9 Solutions