March 5
section covered in text:
2.4. Continuity
objective: to understand the basic
definitions of continuity, to understand the Intermediate Value Theorem
key ideas and/or vocabulary
continuous at a number a, discontinuous, removable
discontinuities, infinite discontinuity, jump discontinuities, continuous
on an interval
definition of a continuous function at a number
a
Theorem 4. continuous functions
Theorem 5. polynomials are continuous everywhere
sine and cosine are continuous functions
inverse functions of continuous functions are continuous
Theorem 7. list of continuous functions
Theorem 8. when the limit symbol can be moved through the function
symbol
Theorem 9. continuity of composition of functions
Theorem 10. Intermediate Value Theorem
solved problems - using key ideas
-
give reasons why functions are not continuous, #3
-
using definition of continuity and limit laws, #9
-
sketching and analyzing continuity of piecewise functions, #12
-
proving a function continuous on its domain, #20
-
graphically finding discontinuities, #21
-
using continuity to evaluate limits, #24.
-
piecewise function, #27
-
Intermediate Value Theorem, #44,32,36,38.
group work
none
announcements
Homework.#2,4,8,12,18,22,30,34
SOLUTION.
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