# Science:Math Exam Resources/Courses/MATH101/April 2014/Question 01 (e)

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MATH101 April 2014
Other MATH101 Exams

### 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 ${\displaystyle \int _{a}^{b}f(x)dx}$.

The error for the Trapezoid Rule satisfies ${\displaystyle |E_{T}|\leq {\frac {K(b-a)^{3}}{12n^{2}}}}$, where ${\displaystyle |f''(x)|\leq K}$ for ${\displaystyle a\leq x\leq b}$. If ${\displaystyle -2 for ${\displaystyle 1\leq x\leq 4}$, find a value of ${\displaystyle n}$ to guarantee the Trapezoid Rule will give an approximation for ${\displaystyle \int _{1}^{4}f(x)dx}$ with absolute error, ${\displaystyle |E_{T}|}$, less than ${\displaystyle 0.001}$.

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