HolcombMath

Tuesday, June 02, 2009

Intro to Calculus (Class 87)

Lesson Title
Lesson for HW 29 (2): Continuity and the Intermediate Value Theorem

Overview
The opener is given over to students to continue their work on Workshop 27. The lesson will focus on finishing up Lesson for HW 29- Continuity and the Intermediate Value Theorem. As time permits, students may begin their work on the Lesson for HW 30 which is computer based.
Textbook Sections
§2.4 (Txt. p.107) Continuity

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
area
definite integral
polar graph
Cartesian

Key Attitudes
Math is about using what you know to create something new.

Key Ideas
A function is continuous if it’s graph can be drawn without lifting the pencil.
In order to analytically determine if a function is continuous at a point, the left-hand and right-hand limit must be equal and the value of the function at the point in question must be equal to this limit.
If a function is continuous on some closed interval, [a,b], then the function takes on every value between f(a) and f(b).
Key Skills
I can explain what it means for a function to be continuous.
I can determine if a function is continuous at a point.
I can determine if a function is continuous on the domain in which it is defined.
I can explain the Intermediate Value Theorem.
I can use the Intermediate Value Theorem to solve problems.
Turn-In (#86)
HW 29 #1-5

Handouts
Monk Problem Solution
HW 29 Continuity and the Intermediate Value Theorem

Assignment
Finish HW 29
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.