Post on 11-Jan-2016
transcript
Evaluating Limits Analytically
1. Use a graphing utility to graph the function and visually estimate
the limits
)(lim)(
)(lim)(
3)(
1
3
xfb
xfa
xxxf
x
x
2. Find the limit
xxx
3lim 2
3
3. Find the limit
x
xx 3
14lim
1
4. Find the limit
xx
x
31
31
lim4
5. Find the limit
xx
tanlim3
6. Find the limit
6csclim
9
xx
7. Find the limit
)((lim)(
)(lim)(
)(lim)(
1)(,3)(
2
3
2
2
xfgc
xgb
xfa
xxgxxf
x
x
x
8. Use the information to evaluate the limits
)(
)(lim)(
)()(lim)(
)()(lim)(
)(5lim)(
4)(lim
8)(lim
xg
xfd
xgxfc
xgxfb
xfa
xg
xf
cx
cx
cx
cx
cx
cx
9. Use the graph to determine the limit visually (if it exists). Write a simpler function that
agrees with the given function at all but one point.
)(lim)(
)(lim)(2
)(
0
3
2
xfb
xfaxx
xxf
x
x
10. Find the limit of the function (if it exists). Write a simpler function that
agrees with the given function at all but one point.
4
492lim
2
4 x
xxx
11. Find the limit of the function (if it exists). Write a simpler function that
agrees with the given function at all but one point.
9
214lim
2
2
3 x
xxx
12. Find the limit (if it exists)
7
32lim
7 x
xx
13. Find the limit (if it exists)
xx
x
61
61
lim0
14. Find the limit (if it exists)
x
xxxxxxx
)2()(2)(lim
22
0
15. Determine the limit of the transcendental function (if it exists)
x
x
xx
cos99lim
0
16. Determine the limit of the transcendental function (if it exists)
csc
1lim
0
17. Determine the limit of the transcendental function (if it exists)
xxx 20 cot
5lim
18. Determine the limit of the transcendental function (if it exists)
1
)1(5lim
2
0 x
x
x e
e
3)(
:for
)()(
lim:0
xxf
x
xfxxfFind
x
19. (similar to p.88 #91-94)
xxfx
c
where
xfcx
3)(3
0
)(lim
20. Use the Squeeze Theorem to find the limit
(similar to p.88 #95-96)