1,001 Calculus Practice Problems For Dummies
viii
Amplitude, Period, Phase Shift, and Midline .............................................. 23
Equations of Periodic Functions .................................................................. 23
Inverse Trigonometric Function Basics ...................................................... 26
Solving Trigonometric Equations using Inverses ...................................... 26
Chapter 3: Limits and Rates of Change . . . . . . . . . . . . . . . . . . . . . . . . . . .29
The Problems You’ll Work On ..................................................................... 29
What to Watch Out For ................................................................................. 29
Finding Limits from Graphs .......................................................................... 30
Evaluating Limits ........................................................................................... 31
Applying the Squeeze Theorem ................................................................... 32
Evaluating Trigonometric Limits ................................................................. 33
Infinite Limits ................................................................................................. 33
Limits from Graphs ........................................................................................ 36
Limits at Infinity ............................................................................................. 37
Horizontal Asymptotes ................................................................................. 38
Classifying Discontinuities ........................................................................... 38
Continuity and Discontinuities .................................................................... 39
Making a Function Continuous .................................................................... 40
The Intermediate Value Theorem ............................................................... 41
Chapter 4: Derivative Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43
The Problems You’ll Work On ..................................................................... 43
What to Watch Out For ................................................................................. 43
Determining Differentiability from a Graph ............................................... 44
Finding the Derivative by Using the Definition .......................................... 45
Finding the Value of the Derivative Using a Graph ................................... 46
Using the Power Rule to Find Derivatives .................................................. 47
Finding All Points on a Graph Where Tangent Lines
Have a Given Value .................................................................................... 48
Chapter 5: The Product, Quotient, and Chain Rules . . . . . . . . . . . . . . . .49
The Problems You’ll Work On ..................................................................... 49
What to Watch Out For ................................................................................. 49
Using the Product Rule to Find Derivatives ............................................... 50
Using the Quotient Rule to Find Derivatives .............................................. 51
Using the Chain Rule to Find Derivatives ................................................... 52
More Challenging Chain Rule Problems ..................................................... 53
Chapter 6: Exponential and Logarithmic Functions
and Tangent Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55
The Problems You’ll Work On ..................................................................... 55
What to Watch Out For ................................................................................. 55
Derivatives Involving Logarithmic Functions ............................................ 56
Logarithmic Differentiation to Find the Derivative ................................... 56
Finding Derivatives of Functions Involving
Exponential Functions ............................................................................... 57
Finding Equations of Tangent Lines ............................................................ 57
Finding Equations of Normal Lines ............................................................. 58
viii