2.5 evaluating limits algebraically fri sept 18 do now evaluate the limits 1) 2)
DESCRIPTION
Rewriting Limits Because limits only depend on values that lead up to x, we can rewrite functions and not affect the limitTRANSCRIPT
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