Unit One

# Limits and Derivatives

Unit Objective:
Understand the concept of limits, continuity, slope of a tangent line, definition of a derivative, rate of change, and derivative of polynomials. Learn and be able to apply the basic rules for finding the derivative. This unit should take no more than 2 weeks to complete.

*All assignments are in Basic Technical Mathematics With Calculus 7th edition by Allyn J. Washington, 2000.

Method of Evaluation:
The unit test will be a pencil and paper quiz taken at your class site. The test will be administered by the instructor or by a proctor. Please see the course schedule for the exact time and date of the unit test.

Objective One
Understand the concept of continuity and limit.
Note: Function rule is not continuous when the denominator is zero.

• Complete Work Exercises 23.1, pages 634-635 #1-19 odd, 23-43 odd.
• Quick Review sheet 1-1.

Objective Two
Be able to find the slope of a secant line and the slope of a tangent line.

Objective Three
Learn the definition of the derivative and how to use it. Know the different notations for the derivative.

• Complete Work Exercises 23.3, pages 643-644 #1-19 odd, 25-29 odd.
• Quick Review sheet 1-3.

Objective Four
Be able to determine the instantaneous rate of change of a function.

• Complete Work Exercises 23.4, pages 647-648 #3,11,13,21,23,25,29.
• Quick Review sheet 1-4.

Objective Five
Be able to find the derivative using the basic rules:

a)

b)

c)

d)

• Complete Work Exercises 23.5, pages 652-653 #1-37 odd, 41,46.
• Quick Review sheet 1-5.

Unit Review

• Review Exercises, pages 671-673 #1-23 odd, 37,49,55.
• Practice Test, page 673 #1,2,3,8.

Worksheets