Write down the first three terms of the Taylor series expansions of the functions dx (t...

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Write down the first three terms of the Taylor series expansions of the functions dx (t + h) and dt about x(t). Use these two equations to eliminate dx (t) and d'x (1) dr dt dx (t-h) dt from the Taylor series expansion of the function x(t + h) about x(t). Show that the resulting formula for x(t + h) is the third member of the Adams- Moulton family, and hence confirm that this Adams-Moulton method is a third-order method. Write down the first three terms of the Taylor series expansions of the functions dx (t + h) and dt about x(t). Use these two equations to eliminate dx (t) and d'x (1) dr dt dx (t-h) dt from the Taylor series expansion of the function x(t + h) about x(t). Show that the resulting formula for x(t + h) is the third member of the Adams- Moulton family, and hence confirm that this Adams-Moulton method is a third-order method.

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