15-1
Tuesday, February 28, 2017
9:30 AM
Clicker Question #1:
The limit of the numerator is not zero, the limit of
the denominator is zero. Therefore there is no
finite limit.
Clicker Question #2:
Reminder:
1. The study guide for Test #2 has been posted.
2. The review session will be on Thursday, 3/2.
3. Test #2 is on March 14 (first Tuesday after spring
break)
Class 15 Page 1
15-2
Tuesday, February 28, 2017
9:47 AM
Different types of discontinuities:
Safe on top of the hill: continuity
Limit exists but not equal to the value
of the function: pothole
The road caved in: no limit.
Class 15 Page 2
15-3
Tuesday, February 28, 2017
10:05 AM
Class 15 Page 3
15-4
Tuesday, February 28, 2017
10:21 AM
1. Only need to check the points where different
Parts of the function connect.
2.
f(x) is continuous at x=1
3.
Class 15 Page 4
f(x) is continuous at x=3 from the left.
Class 15 Page 5
15-5
Tuesday, February 28, 2017
10:37 AM
Intermediate Value Theorem
If f(x) is continuous on [a,b] and f(a) < f(b), then
every value between f(a) and f(b) is taken by the
function f somewhere on [a,b].
Class 15 Page 6