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Final

MATH 2B Study Guide - Final Guide: Cubic Function, Limit Comparison Test, Direct Comparison TestPremium


Department
Mathematics
Course Code
MATH 2B
Professor
Timmy Ma
Study Guide
Final

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University of California
Irvine
MATH 2B
Single-Variable Calculus
Fall 2017
Final Exam
Prof: Timmy Ma
Exam Guide

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CONTENTS
Exam Guide Covers the Following Topics:
Chapter 11
11.2 - Series
11.3 - Integral Test
11.4 - Comparison Test
11.5 - Alternating Series Test
11.6.1 - Absolute Convergence
11.6.2 - Ratio and Root Tests
11.7 - Strategy for Testing Series
11.8 - Power Series
11.9 - Representations of Power Series
11.10 - Taylor and Maclaurin Series

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Series
What are series?
.. ..
k=1
ak=a1+a2+a3+ . + an+an+1 + .
When you add everything up, what do you get?
This question is the series convergence check
Add first however many finite numbers
Partial sums
bn= ∑
n
k=1
ak
What does this mean?
The nth partial sum is the sum of first n terms
A series converges if is a number lim
n→∞ bn
Example #1
Think of a cake
Day 1: you eat ½ of the cake = a1
Day 2: you eat half of the remaining half, which is ¼ of the cake = a2
Day 3: you eat half of the remaining half, which is of the cake = a3
Day 4: repeat; 1/16 of the cake = a4
Day n: =
1
2nan
Check after finite amount of days using an
Total cake eaten is partial sum
/2d1= 1
/2 /4 /4d2= 1 + 1 = 3
/2 /4 /8 /8d3= 1 + 1 + 1 = 7
dn= ∑
n
k=1
1
2k= 1 − 1
2n
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