161workbook - Calculus Workbook Compiled by Jerry Morris...

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Calculus Workbook Compiled by: Jerry Morris, Sonoma State University Note to Students: (Please Read) This workbook contains ex- amples and exercises that will be referred to regularly during class. Please purchase or print out the rest of the workbook before our next class and bring it to class with you every day. 1. To Purchase the Workbook. Go to Digi-Type , the print shop at 1726 E. Cotati Avenue (across from campus, in the strip mall behind the Seven-Eleven). Ask for the workbook for Math 161 - Calculus 1. The copying charge will probably be between $10.00 and $20.00. You can also visit the Digi-Type webpage () to order your workbook ahead of time for pick-up. 2. To Print Out the Workbook. Go to the Moodle page for our course and click on the link “Math 161 Workbook”, which will open the Fle containing the workbook as a .pdf Fle. BE ±OREWARNED THAT THERE ARE LOTS O± PICTURES AND MATH ±ONTS IN THE WORKBOOK, SO SOME PRINTERS MAY NOT ACCURATELY PRINT PORTIONS O± THE WORKBOOK. If you do choose to try to print it, please leave yourself enough time to purchase the workbook before our next class class in case your printing attempt is unsuccessful.
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2 Sonoma State University Table of Contents Review Examples . ............................................................................. 3 Preliminary Review Problems . ................................................................. 4 Chapter 2 – Limits and Derivatives Section 2.2 – The Limit of a Function . ........................................................ 5 Section 2.3 – Limit Laws . ..................................................................... 8 Section 2.4 – Continuity . .................................................................... 12 Section 2.5 – Limits Involving In±nity . ....................................................... 15 Sections 2.1/2.6 – Tangents, Velocities, and Other Rates of Change . .......................... 19 Section 2.7 – Derivatives . .................................................................... 22 Section 2.8 – The Derivative as a Function . .................................................. 25 Section 2.9 – What does f say about f ? ..................................................... 29 Chapter 3 – DiFerentiation Rules Section 3.1 – Derivatives of Polynomials and Exponential Functions . ......................... 33 Section 3.2 – Product and Quotient Rule . .................................................... 37 Section 3.3 – Rates of Change in the Natural and Social Sciences . ............................ 41 Sections 3.4/3.5 – The Chain Rule and Trigonometric Functions . ............................. 43 Section 3.6 – Implicit Di²erentiation . ........................................................ 49 Section 3.7 – Derivatives of Logarithmic Functions . .......................................... 53 Section 3.8 – Di²erentials and Linear Approximations . ....................................... 57 Chapter 4 – Applications of DiFerentiation Section 4.1 – Related Rates . ................................................................. 61 Sections 4.2/4.3 – Information Summary . .................................................... 65 Section 4.2 – Maximum and Minimum Values . ............................................... 65 Section 4.3 – Derivatives and the Shapes of Curves . .......................................... 68 Section 4.5 – Indeterminate Forms and L’Hospital’s Rule . .................................... 75 Section 4.6 – Optimization Problems . ........................................................ 78 Section 4.8 – Newton’s Method . ............................................................. 86 Section 4.9 – Antiderivative Problems . ....................................................... 88 Chapter 5 – Integrals Section 5.1 – Areas and Distances . ........................................................... 93 Section 5.2 – The De±nite Integral . .......................................................... 95 Section 5.2 – Integration Practice . ........................................................... 98 Section 5.3 – Evaluating De±nite Integrals . ................................................. 101 Section 5.4 – The Fundamental Theorem of Calculus . ....................................... 105 Section 5.5 – The Substitution Rule . ........................................................ 109
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Calculus Workbook 3 Math 161 – Review Examples Example 1. Let f ( x ) = x x + 1 .
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