Embed Size (px)
Citation preview
Review Limits
When you see the words…This is what you think of doing…
f is continuous at x = a
Test each of the following
1
lim ( ) existsx a
f x
( ) existsf a
lim ( ) ( )x a
f x f a
Review Limits
When you see the words… This is what you know…
f has an infinite discontinuity at x = a
* lim ( ) or limis x a x a
f x
2
Review Limits
When you see the words… This is what you know…
f has a jump discontinuity at x = a
-
3
lim ( ) and lim ( ) both exist,
but are not equalx a x a
f x f x
Review Limits
When you see the words… This is what you know…
f has a removable discontinuity at x = a
-
4
lim ( ) but does not equal f (a)x a
f x
Review Limits
When you see the words… This is what you know…
Squeeze Theorem If f(x) <= g(x) < h(x) and
5
lim ( ) lim ( )
then
lim ( )
x c x c
x c
f x h x
g x L
Review Limits
When you see the words… This is what you know…
Intermediate Value Theorem
If f is continuous on [a,b] and k is between f(a) and f(b), then there exists a c in [a,b] such that f( c ) = k
6
Review Limits
When you see the words… This is what you know…
Extreme Value Theorem
f has a maximum and a minimum value in the interval [a, b]
7
Review Limits
When you see the words… This is what you know…
The graph of f has a horizontal asymptote at y = k
-
8
lim ( )x
f x k
Review Limits
When you see the words… This is what you know…
The graph of f has a vertical asymptote at
x = a
-
9
lim ( )x a
f x
Review Limits
When you see the words… This is what you know…
- 1
10
0
sinlimx
xx
Review Limits
When you see the words… This is what you know…
- 0
11
sinlimx
xx
Review Limits
When you see the words… This is what you know…
- Does not exist
12
0
1limx x
Review Limits
When you see the words… This is what you know…
- 0
13
0
cos 1limx
xx
Review Limits
When you see the words… This is what you know…
- e
14
1lim 1
n
x n
Review Limits
When you see the words… This is what you know…
- Lim does not exist
15
I f lim ( ) lim ( ),
then ...x a x a
f x f x
Review Limits
When you see the words… This is what you know…
- 1
16
lim
n
nn
