$\"\"$

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(a)

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The definite integral is $\"\"$ .

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Let $\"\"$ .

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The first derivative is $\"\"$ .

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The second derivative is $\"\"$ .

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The maximum value of $\"\"$ on the interval $\"\"$ is

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$\"\"$

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Approximate error in trapezoidal rule $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Obtain an error $\"\"$ that is less than $\"\"$ , choose $\"\"$ such that $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The value of $\"\"$ in trapezoidal rule is $\"\"$ .

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$\"\"$

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(b)

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The function is $\"\"$ .

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The first derivative is $\"\"$ .

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The second derivative is $\"\"$ .

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The third derivative is $\"\"$ .

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The fourth derivative is $\"\"$ .

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The maximum value of $\"\"$ on the interval $\"\"$ is $\"\"$ .

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Approximate error in Simpsons rule $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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Obtain an error $\"\"$ that is less than $\"\"$ ,choose $\"\"$ such that $\"\"$ .

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$\"\"$

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$\"\"$ .

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In Simpsons Rule $\"\"$ must be even number, so round up to the next even integer.

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The value of $\"\"$ in Simpsons rule is $\"\"$ .

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$\"\"$

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(a) The value of $\"\"$ in trapezoidal rule is $\"\"$ .

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(b) The value of $\"\"$ in Simpsons rule is $\"\"$ .