2.5 Evaluating Limits Algebraically Fri Sept 18 Do Now Evaluate the limits 1) 2)

HW Review p.80 #1-19 odds 1) 917) 1/5 3) 1/1619) 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, odds

Review Tues Sept 22 Do Now - Evaluate each limit

HW Review: p.94 #5-41 5) 1/1423) 2 7) -125) 1/4 9) 11/1027) 1 11) 229) 9 13) 131) sqrt2 / 2 15) 233) 1/2 17) 1/837) 12 19) 7/1739) -1 21) DNE41) 4/3

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? Quiz Thurs Sept 24