Calculus I

Tuesday, September, 30, 2008

Objective: The student will be able to:
Apply properties of continuous functions
Apply theorem of composite function
Apply intermediate value theorem for continuous theorem
Agenda:
I. Test Review
II. Examples of the properties
III. What is the intermediate theorem for continuous functions and what are its consequences. ( Graphing and problem solving)
IV. Homework Review

Homework: Page 80 to 81: 29 through 45

Answers: to last 2-28
It is continuous except at x=1 and x=3. Both are infinite discontinuities
4. The function is a compostition of x-1 and the absolute value function. Both are continuous with a domain of all reals so there are no discontinuities.
6. The function is a compostion of two continuous functions . No points of discontinuities.
8. The function is equivalent to the cos/sin . Both are continuous, but it does have inifinte discontinuities at x=k
10. There are no points of discontinuity unless you go outside the domain x<1.
12. a. Yes 1
b. Yes 2
c. No
d. No
14. Everywhere in [ -1,3) except for x=0,1,2
16. Since then we should assign f(1) =2
18. Assign the value 0 to f(3). Since 3 is a right endpoint , the function (extended) is continuous at 3.

20. a. x=2 b. Not removable

22. a. x=-1 b. Removable , assign the value 0 to f(-1)

24. a. All points not in the domain along with x=1,2
b. x=1 is not removable because the limits as you approach from both sides is different. X=2 us removable by assigning f(2)=1