15. (a) Calculate e with an error of less than 10-6. (b) Estimate the error in the approximation sinh(x) = x + (x³/3!) when || < 0.5. (c) How close is the approximation sin(x) = x when || < 10-³? For which of these values of x is x < sin(x)?

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A: Given that      f"(x)= -36sin(6x) , f'(0)=6 and f(0)=0 .

Q: 4. f(x) = 4x3x =

A: Please see the below picture for detailed solution.

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A: Given:

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A:

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A: We have to find the given derivative ddx∫0x5sin t dt.

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A:

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A:

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A: Given data:     The given expression for the integral of the function is: .   The expression for the…

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A:

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A:

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A: I have appended the formula used in the solution part of the question

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A: In this question, we want to compute the value of f at the given point.

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A: We can solve this as follows:

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A: w