2.6 Trigonometric Limits Tues Sept 23 Do Now Evaluate the limits

HW Review p.94 #1-17 37 39 • 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:

• Evaluate EX 2

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 • 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) lim

x

® 2 [(

x

2)cos( 1

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)

• P.94

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

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 • 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 • 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