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

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15 Sep 2018

School

Department

Course

Professor

Miami University

MTH 251

Calculus II

Winter 2018

Term Test 3

Professor: Konstantinos Beros

Exam Guide

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

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 simpson’s rule,