Write down the first four terms of the Taylor series expansion of the function x(t-h) about x(t), and the first three terms of the expansion of the function (t-h) dt about x(t). Use these two equations to eliminate d²x (1) (1) and d' d³x (1) dt³ dt² from the Taylor series expansion of the function x(t + h) about x(t). Show that the resulting formula is Xn+1 = -4X₁ + 5X-1 + h(4F + 2F-1) + O(h*) Show that this method is a linear combination of the second-order Adams-Bashforth method and the central difference method (that is, the scheme based on (2.9)). What do you think, in view of this, might be its disadvantages?

Q: Confirm that summation d/36 ϕ(d) = 36 and summation d/36 (-1)^(36/d) ϕ(d) = 0

A: We have to confirm that ∑d/36φ(d)=36 and ∑d/36(-1)36/dφ(d)=0.

Q: Suppose the function f(x) has a Taylor series at I = 4 that converges to f(x) for all a € R, and the…

A: The given function fx has a Taylor series at x=4 that converges for all x∈ℝ and the nth derivative…

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Q: Find the coefficient of the term containing x' in the expansion of (2x-y)°.

A: Binomial theorem

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