PreCalculus

Chapter 5 Limits & Derivatives

Unit 5-1 The Indeterminate Forms and Limits

Standard 5a: Evaluate limits involving the indeterminate form 0/0

Agenda

Screencast Review: What is a Limit?

How to find a limit graphically
How to find a limit analytically
How will we use limits?

Indeterminate Forms & Factoring to Find Limits
Desmos Activity
Assignment 5-1: Pg 294 #1-6, 10-14

Unit 5-2 Slope of a Tangent Line

Standard 5b: Find the derivative (slope of the tangent line) of a polynomial function at a given point
Standard 5c: Use the limit definition to find the derivative of a polynomial function

Agenda

Secant Line to Tangent Line Slopes

Using the Limit Definition
Using the Derivative at a Point Formula

Tangent Line Slopes
Assignment 5-2: Pg 302 #1-4, 9-13

Unit 5-3 The Power Rule

Standard 5d: Find the derivative of a polynomial function using the Power Rule

Agenda

Using the Power Rule to Differentiate a Polynomial
Assignment 5-3: Pg 309 #1-10

Unit 5-4 Tangent Lines & Local Linearity

Standard 5e: Find the equation of the tangent and normal lines to a polynomial function at a given point
Standard 5f: Use the equation of the tangent line to approximate function values

Agenda

Finding the Equation of a Tangent Line to a Polynomial
Finding the Equation of a Normal Line to a Polynomial
Using the Tangent Line to Approximate Function Values
Assignment 5-4: Part A Pg 317 #1-8 Part B Pg #9-12

Unit 5-5 Rectilinear Motion: Position, Velocity, & Acceleration

Standard 5g: Given the position function of an object as a polynomial, use the derivative to find the velocity and acceleration functions
Standard 5h: Use sign patterns to describe the motion of an object

Agenda

One Dimensional Motion

Position or Height of an Object
Velocity as the Derivative of Position
Acceleration as the Second Derivative of Position

Finding the Speed of an object; the difference between speed and velocity.
Finding the time and position at which an object changes directions
Assignment 5-5: Pg 326 #1-13