2.5 Evaluating Limits AlgebraicallyFri Sept 18

Do NowEvaluate the limits

1)

2)

HW Review p.80 #1-19 odds

• 1) 9 17) 1/5• 3) 1/16 19) 1/5• 5) 1/2• 7) 4.6• 9) 1• 11) 9• 13) -2/5• 15) 10

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:

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

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 ReviewTues Sept 22

• Do Now - Evaluate each limit

HW Review: p.94 #5-41

• 5) 1/14 23) 2• 7) -1 25) 1/4• 9) 11/10 27) 1• 11) 2 29) 9• 13) 1 31) sqrt2 / 2• 15) 2 33) 1/2• 17) 1/8 37) 12• 19) 7/17 39) -1• 21) DNE 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