2.6 Trigonometric Limits Fri Sept 25 Do Now Evaluate the limits.

2.6 Trigonometric LimitsFri Sept 25

Do Now

Evaluate the limits

HW Review p.94 #1-17 37 39

• 1) 12 17) 1/8• 3) 0 37) 12• 5) 1/14 39) -1• 7) -1• 9) 11/10• 11) 2• 13) 1• 15) 2

Factoring Trigonometric Limits

• Rewriting limits in terms of sinx and cosx can help to eliminate factors

• EX:

EX 2

• Evaluate

The Squeeze Theorem

• Suppose thatfor all x in some interval (c,d), and that

where L is a numberThen, 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)

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 Wed

2-3 2-5 2-6 ReviewMon Sept 28

• Do Now

• Evaluate each limit

• 1)

• 2)

HW Review:• P.94• 27) 1• 28) 0• P. 99• 7) 0• 8) 0• 9) 0• 11) 0

Quiz Review (On Fri)

• 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 ReviewTues Sept 29

• Find the limit of each

Worksheet p. 100 5-27 odds

• 5) 1 19) 0

• 7) 7^(1/2) 21) 2

• 9) -3/8 23) 2

• 11) 5 25) 9

• 13) 3/4 27) 4

• 15) 3/4

• 17) 1

HW Review p.100 6-26 evens

• 6) -1 20) e

• 8) 5^(1/3) 24) 1/4

• 10) -1/4 26) 0

• 12) -3 22) 1

• 14) -1/3

• 16) 1/6

• 18) -1

Closure

• Besides plugging in values, what limit method do you like best? Worst? Why?

• 2.3, 2.5, 2.6 Quiz Wed