Transcript 2.6 Trigonometric Limits Mon Sep 24

2.6 Trigonometric Limits
Tues Sept 23
Do Now
Evaluate the limits
HW Review p.94 #1-17 37 39
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1) 12
3) 0
5) 1/14
7) -1
9) 11/10
11) 2
13) 1
15) 2
17) 1/8
37) 12
39) -1
Factoring Trigonometric Limits
• Rewriting limits in terms of sinx and
cosx can help to eliminate factors
• EX:
EX 2
• Evaluate
The Squeeze Theorem
• Suppose that f (x) £ g(x) £ h(x)
for all x in some interval (c,d), and that
where L is a number
Then, it follows that
• Since g(x) is “squeezed” by the other 2
functions, its limit must be the same.
Squeeze Theorem
• This theorem is good for products with
sinx and cosx, because we know the
range
• EX:
Ex 2
• Evaluate using the Squeeze Theorem
You Try
• Evaluate the limits
• 1)
• 2)
• 3)
• 4)
1
lim[(x - 2)cos( x-2
)]
x®2
Closure
• What kind of methods can we use to
help evaluate limits? Describe one.
• HW: p.94 #27 28 p.99 #7 8 9 11
– 2.3 2.5 2.6 Quiz Friday
2-3 2-5 2-6 Review
Wed Sept 24
• Do Now
• Evaluate each limit
• 1)
• 2)
HW Review:
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P.94
27) 1
28) 0
P. 99
7) 0
8) 0
9) 0
11) 0
Quiz Review (On)
• Ways to evaluate a limit:
– Plug into function (IF DEFINED)
– Factor and cancel undefined factor
– Multiply by conjugates
– Squeeze Theorem
– Graph/Table (may not be accurate)
Practice
• (Green book) Worksheet p.100 #5-24
Limit Review
Wed Sept 25
• Find the limit of each
Worksheet p. 100 5-27 odds
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5) 1
7) 7^(1/2)
9) -3/8
11) 5
13) 3/4
15) 3/4
17) 1
19) 0
21) 2
23) 2
25) 9
27) 4
HW Review p.100 6-26 evens
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6) -1
8) 5^(1/3)
10) -1/4
12) -3
14) -1/3
16) 1/6
18) -1
20) e
24) 1/4
26) 0
22) 1
Closure
• Besides plugging in values, what limit
method do you like best? Worst? Why?
• 2.3, 2.5, 2.6 Quiz Friday