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MCV4U-A 3 Unit Applying Derivatives and Introduction to Vectors
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Copyright © 2008 The Ontario Educational Communications Authority. All rights reserved. No part of these materials may be reproduced, in whole or in part, in any form or by any means, electronic or mechanical, including photocopying, recording, or stored in an information or retrieval system, without the prior written permission of The Ontario Educational Communications Authority. Every reasonable care has been taken to trace and acknowledge ownership of copyright material. The Independent Learning Centre welcomes information that might rectify any errors or omissions. December 6, 2010
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Calculus and Vectors MCV4U-A Unit 3 Introduction, page 1 Copyright © 2008 The Ontario Educational Communications Authority. All rights reserved. You are here Table of Contents Unit 1: Rates of Change and Derivatives Lesson 1: Rates of Change Lesson 2: Limits Lesson 3: Intervals of Increase and Decrease Lesson 4: Derivative of a Polynomial Function Lesson 5: Properties of the Derivative Suggested Answers to Support Questions Unit 2: Exploring Derivatives Lesson 6: Exploring Exponential Functions and Their Derivatives Lesson 7: The Derivatives of Sinusoidal and Rational Functions Lesson 8: The Second Derivative: A Graphical Look Lesson 9: Applications of the Derivative: Key Features of a Polynomial Function Lesson 10: Sketching Functions Suggested Answers to Support Questions Unit 3: Applying Derivatives and Introduction to Vectors Lesson 11: Real-Life Applications Lesson 12: Optimization Problems Lesson 13: Introduction to Vectors Lesson 14: Vectors in Three-Space, Addition and Subtraction Lesson 15: Properties of Vectors and Scalar Multiplication Suggested Answers to Support Questions Unit 4: Lines and Planes Lesson 16: The Dot and Cross Product of Two Vectors Lesson 17: Properties and Applications of Dot and Cross Products Lesson 18: Lines and Planes Using Linear Equations Lesson 19: Representations of Lines and Planes Using Scalar, Vector, and Parametric Equations Lesson 20: Intersections Suggested Answers to Support Questions
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Unit 3 Introduction, page 2 Calculus and Vectors MCV4U-A Copyright © 2008 The Ontario Educational Communications Authority. All rights reserved. Introduction In this unit, you will complete the calculus portion of the course and begin looking at vectors. In the first two lessons, you will learn about applications of derivatives. For example, suppose you want to find the minimum amount of material to use to build a box of a specific volume. This is called an optimization problem. You learned earlier in the course that derivatives help you study the rate of change and how the change in one variable leads to the change in a dependent variable. You also learned that the derivative of a function helps determine the maximum and minimum of a function over an interval. In this unit, you will learn how to use your knowledge of calculus to solve a number of optimization problems from the world of science and economics.
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