MTH 251 Study Guide - Midterm Guide: Limit Comparison Test, Geometric Progression, Monotonic Function

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Miami University
MTH 251
Calculus II
Winter 2018
Term Test 3
Professor: Konstantinos Beros
Exam Guide
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Table of content
- Section 7.7: Approximation Of Integrals
- Section 11.1: Sequence
- Section 11.2: Series
- Section 11.3: The Integral Test
- Section 11.4: Comparison Test
- Section 11.5: Alternating Series
- Section 11.6: Absolute Convergence and ratio and root tests
- Section 11.8: Power Series
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Section 7.7: Approximation of Integrals
Recall:
If f is continuous on [,] then,
()
=lim
()

Where =
and =+
The area under the curve can be estimated using right and left midpoints.
The area under the curve can also be estimated using midpoints,
=(),
 where =
(+)
The are under the curve can also be estimated using the trapezoid rule, which is just the
average of the left and right sums added together,
=1
2()+()


=()+()
2+()


Simpson’s Rule:
The final way we will look at to approximate integrals is called simpsons rule,
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