2.5 evaluating limits algebraically fri sept 18 do now evaluate the limits 1) 2)
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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
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