4. Taylor method of order three is given by Yi+1 = Y; +hT(³) (t₁, Y;), where T(³) (t₁, Y;) = f (t¡‚ Yi) + h h² (ti, Yi) + / / f '(t₁, Y) + h ¯¯ ƒ' 3! f " (ti, Yi) Write out this method's formula when it is applied to the IVP: y' = -y + sin t. (The formula expression should have no f, f', or f", it should only involves t, h and y. Do not carry out the actual calculations)

Q: If y = f(x), then f'(x), y', [Select] dy da and f(x) all represent the of fat x.

A: If , then to determine the meaning of .

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A:

Q: Find y as a real-valued function of tif y(5) 9, y'(5) = 9. = y = 49y" 140y + 100y = 0, -

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A: Given data÷

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A: To find f"(t) we integrate f"'(t)

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A:

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A: Solution :-

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A: Please see the below picture for detailed solution.

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A:

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A: INTRODUCTION A function's differentiation can be used to display the rate of change of a function at…

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A:

Q: 8) Suppose you are at the point (2, 1, 82) on the hill given by f(x,y) = 100-4x²-2y (where the z…

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Q: 6. FinD F(S) if f(t)= t· cost

A:

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A: We will solve the problem

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A:

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A: a)   f(x)= 2x3+1f(x+h)= 2(x+h)3+1                         =2(x3+3x2h+3xh2+h3)+1…