Transcript 2.5 Evaluating Limits Algebraically

2.5 Evaluating Limits
Algebraically
Fri Sept 18
Do Now
Evaluate the limits
1)
2)
HW Review p.80 #1-19 odds
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1) 9
3) 1/16
5) 1/2
7) 4.6
9) 1
11) 9
13) -2/5
15) 10
17) 1/5
19) 1/5
Rewriting Limits
• Because limits only depend on values
that lead up to x, we can rewrite
functions and not affect the limit
Indeterminate forms
• A function f(x) has an indeterminate form at
x = c if f(c) yields one of the following:
0 ¥
,
, ¥× 0, ¥ - ¥
0 ¥
Finding a Limit by Factoring
• One method to evaluate limits is to
eliminate factors in the denominator.
• Ex:
EX 2
• Evaluate
Ex 2b
• We can also factor trigonometric limits
Ex 3
• We can rewrite by multiplying by the
conjugate
Ex 4
• Evaluate
Combining Fractions
• We can add two fractions with undefined
values to help cancel
æ 1
2 ö
ç
÷
lim
2
x -1 ø
x®1 è x -1
Infinite but not indeterminate
• Evaluate
You try
• Evaluate each limit
• 1)
• 2)
• 3)
Closure
• What are some methods to evaluate
limits at undefined points? Explain one
of them with an example.
• HW: p.94 #5-33 odds, 37-41 odds
2.3-2.5 Review
Tues Sept 22
• Do Now - Evaluate each limit
HW Review: p.94 #5-41
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5) 1/14
7) -1
9) 11/10
11) 2
13) 1
15) 2
17) 1/8
19) 7/17
21) DNE
23) 2
25) 1/4
27) 1
29) 9
31) sqrt2 / 2
33) 1/2
37) 12
39) -1
41) 4/3
2.3 -2.5 Review
• Quiz tomorrow
• Evaluating Limits
• Continuity
Closure
• What is an indeterminate form? Why do
we try to transform or rewrite functions
that have indeterminate forms when
evaluating limits?
• 2.3-2.5 Quiz Thurs Sept 24