Calculus 12 Workbook
Description
This Calculus Workbook has seminar notes followed by questions to support.
Attached is a solutions package showing answers and detailed answers to some selected questions.
TABLE OF CONTENTS
UNIT 1 - DERIVATIVES
Course Overview ...................................... Pg. 3
1.1 – Differentiability ................................ Pg. 5
1.2 – Product, Quotient, Chain Rules ...... Pg. 14
1.3 – Simplifying using Chain Rule .......... Pg. 29
1.4 – Position, Velocity & Acceleration ... Pg. 32
1.5 – Implicit Differentiation .................... Pg. 34
1.6 – Related Rates ....................................Pg. 39
1.7 – Trigonometric Functions ................. Pg. 45
1.8 – Natural Log & e Functions .............. Pg. 51
1.9 – Exponential & Log Functions .......... Pg. 54
1.10 – Numerical Value Tables ................. Pg. 57
UNIT 2 - INTEGRALS
2.1 – Antiderivatives .................................. Pg. 61
2.2 – U-Substitution ................................... Pg. 70
2.3 – Integration by Parts .......................... Pg. 74
2.4 – Definite Integrals .............................. Pg. 79
2.5 – Area Under Curve x-axis .................. Pg. 83
2.6 - Area Under Curve y-axis ....................Pg. 91
2.7 - Area Between Curves x-axis ............. Pg. 94
2.8 - Area Between Curves y-axis ............. Pg. 106
UNIT 3 - LIMITS
3.1 – The Limit of a Function .................... Pg. 113
3.2 – Evaluating Limits .............................. Pg. 139
3.3 – Definition of a Derivative ................. Pg. 150
3.4 – Limits Involving Trig & e .................. Pg. 155
3.5 – Piece-wise Limit Functions .............. Pg. 158
UNIT 4 – CRITICAL POINTS and
SKETCHING FUNCTIONS
4.1 – Equations of Lines ........................... Pg. 163
4.2 – What’s the Point .............................. Pg. 172
4.3 – Sketching Functions ........................ Pg. 192
4.4 – Position, Velocity & Acceleration ... Pg. 212
4.5 – Sketching Derivatives ...................... Pg. 224
4.6 – Sketching with Conditions .............. Pg. 231
UNIT 5 – Application of Derivative
5.1 – Linear Approximation ..................... Pg. 241
5.2 – Optimization .................................... Pg. 251
5.3 – Riemann’s Sum ................................ Pg. 260
5.4 – Mean Value Theorem, Rolle’s Theorems
& Intermediate Value Theorem ….. Pg. 263
5.5 – Improper Integrals ........................... Pg. 269
5.6 – Complex Numbers .......................... Pg. 276
5.7 – Polar Coordinates ............................ Pg. 279
