Science:Math Exam Resources/Courses/MATH101/April 2014/Question 01 (e)
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Question 01 (e)
Short Problem. Show your work. No credit will be given for the answer without the correct accompanying work.
Consider the Trapezoid Rule for making numerical approximations to .
The error for the Trapezoid Rule satisfies , where for . If for , find a value of to guarantee the Trapezoid Rule will give an approximation for with absolute error, , less than .
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What should , , and be in the Trapezoid Rule?
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First, we have , so and thus in the Trapezoid rule formula. Also, from the integral bounds, , and so , and in the formula.
Thus, using the Trapezoid Rule with these values,
Now, find such that