Page 15 - Calculus Workbook For Dummies

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Table of Contents

Disciplining Those Improper Integrals................................................................................231
Solutions to Integration Application Problems..................................................................234
Chapter 13: Infinite Series: Welcome to the Outer Limits...........................................243
The Nifty nth Term Test .......................................................................................................243
Testing Three Basic Series ...................................................................................................245
Apples and Oranges . . . and Guavas: Three Comparison Tests .....................................247
Ratiocinating the Two “R” Tests...........................................................................................251
He Loves Me, He Loves Me Not: Alternating Series...........................................................253
Solutions to Infinite Series ....................................................................................................255

Part V: The Part of Tens.............................................................263

Chapter 14: Ten Things about Limits, Continuity, and Infinite Series .......................265
The 33333 Mnemonic.............................................................................................................265
First 3 over the “l”: 3 parts to the definition of a limit.............................................265
Fifth 3 over the “l”: 3 cases where a limit fails to exist............................................266
Second 3 over the “i”: 3 parts to the definition of continuity.................................266
Fourth 3 over the “i”: 3 cases where continuity fails to exist.................................266
Third 3 over the “m”: 3 cases where a derivative fails to exist ..............................266
The 13231 Mnemonic.............................................................................................................267
First 1: The nth term test of divergence....................................................................267
Second 1: The nth term test of convergence for alternating series.......................267
First 3: The three tests with names............................................................................267
Second 3: The three comparison tests......................................................................267
The 2 in the middle: The two “R” tests......................................................................267

Chapter 15: Ten Things You Better Remember about Differentiation .......................269
The Difference Quotient........................................................................................................269
The First Derivative Is a Rate ...............................................................................................269
The First Derivative Is a Slope..............................................................................................269
Extrema, Sign Changes, and the First Derivative ...............................................................270
The Second Derivative and Concavity ................................................................................270
Inflection Points and Sign Changes in the Second Derivative..........................................270
The Product Rule ...................................................................................................................270
The Quotient Rule..................................................................................................................270
Linear Approximation............................................................................................................271
“PSST,” Here’s a Good Way to Remember the Derivatives of Trig Functions.................271

Chapter 16: Ten Things to Remember about Integration
If You Know What’s Good for You ....................................................................................273
The Trapezoid Rule................................................................................................................273
The Midpoint Rule .................................................................................................................273
Simpson’s Rule .......................................................................................................................273
The Indefinite Integral ...........................................................................................................274
The Fundamental Theorem of Calculus, Take 1.................................................................274
The Fundamental Theorem of Calculus, Take 2.................................................................274
The Definite Integral ..............................................................................................................274
A Rectangle’s Height Equals Top Minus Bottom................................................................274
Area Below the x-Axis Is Negative........................................................................................275
Integrate in Chunks................................................................................................................275
Index .......................................................................................277