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

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Write down the first three terms of the Taylor series expansions of the functions dx dt about x(t). Use these two equations to eliminate dx (t) and dt dx (t (t-h) and (t-2h) 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- Bashforth family, and hence confirm that this Adams-Bashforth method is a third-order method. Write down the first three terms of the Taylor series expansions of the functions dx dt about x(t). Use these two equations to eliminate dx (t) and dt dx (t (t-h) and (t-2h) 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- Bashforth family, and hence confirm that this Adams-Bashforth method is a third-order method.

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