Friday, May 29, 2009
Intro to Calculus (Class 86)
Announcements
Test on Limits this Friday.
Lesson Title
Lesson for HW 29 (1): Continuity and the Intermediate Value Theorem
Overview
Class today will be begin with a puzzle that leads us into a closer inspection of what it means for a function to be continuous and examine an implication of continuity. This implication, the Intermediate Value Theorem, will provide us a new tool which (surprisingly) can be used to help solve the puzzle. During the last 45 minutes of class students will work Test 8 focusing on limits.
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 (#85)
WS 27 #1-4
Handouts
Lesson for HW 29
HW 29
Assignment
HW 29 #1-5
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.
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