1.5 limits calculus 9/16/14. warm-up limits – p. 49
TRANSCRIPT
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1.5 LIMITSCalculus 9/16/14
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WARM-UP
• 1. What is the domain and range:
2. Evaluate the expression and simplify ,
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LIMITS – P. 49
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GOAL
•Find limits graphically or numerically•Use properties of limits and analytic techniques to evaluate limits of a function
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DEFINITION
•Limit of a Function – If becomes arbitrarily close to a single number as approaches from either side, then
“the limit of as approaches c is ”
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FINDING A LIMIT•Direct Substitution:
•
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EX. 1
•
a) c) graph
b) Table
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EXAMPLE 2.•
•
• table
•Graph
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EXAMPLE 3
• table
•Graph
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EX. 3
• Graph
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FIND THE LIMIT
lim𝑥→ 1
𝑥3+4 𝑥−5𝑥−1
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PROPERTIES –P.51
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OPERATIONS
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EX 6- FIND THE LIMIT
lim𝑥→ 2
𝑥2+2 𝑥−3
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WARM-UP•Graph
•What does the graph look like and why?
•When does a limit not exist?
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LIMTS•Limits are useful when we need to find the value of a function getting close to a certain “x” value•We can use direct substitution (“plug in” the x to find the value at that point), but sometimes that is not possible and limits help us see what the function value could be as we approach that x value
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FIND THE LIMIT
•
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FIND THE LIMIT
lim𝑥→ 1
𝑥3−1𝑥−1
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ONE- SIDED LIMITS
•
lim𝑥→ 0+¿|2 𝑥|
𝑥¿
¿
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DOES THE LIMIT EXIST OR NOT?
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FIND A ONE-SIDED LIMIT
• Find the limit of f(x) as x approaches 1
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UNBOUNDED BEHAVIOR
lim𝑥→ 2
3𝑥−2
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COMPARING ONE SIDED LIMITS
•Ex. 9 in the book.