pre cal 12-2 lesson with notes...
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Pre Cal 122 lesson with notes 5th.notebook
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122 Evaluating Limits Algebraically
Daily Outcomes:I can evaluate limits of polynomial and rational functions at
selected pointsI can evaluate limits of polynomial and rational functions at
infinity
What limit does x approach when the light is at its minimum? maximum?
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Pre Cal 122 lesson with notes 5th.notebook
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May 09, 2017
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Pre Cal 122 lesson with notes 5th.notebook
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Example 1: Use the properties of limits to evaluate each limit.
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Pre Cal 122 lesson with notes 5th.notebook
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Use the properties of limits to evaluate each limit.
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Pre Cal 122 lesson with notes 5th.notebook
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Basically, direct substitution can be used to evaluate the limit of a function as long as the denominator, when evaluated, is not 0, or when there is a negative under the square root.
Example 2: Use direct substitution, if possible, to evaluate each limit. If not possible, explain why not.
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Pre Cal 122 lesson with notes 5th.notebook
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Use direct substitution, if possible, to evaluate each limit. If not possible, explain why not.
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Pre Cal 122 lesson with notes 5th.notebook
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Dec 135:33 AM
Indeterminate form: 0/0, when this result is obtained by direct substitution, you cannot determine the limit by this method. This just means you may or may not have a limit so try another method.
Factoring and dividing out any common factor:
Example 3: Evaluate each limit.
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Pre Cal 122 lesson with notes 5th.notebook
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When dividing out a common factor, the result is a new function. The two functions yield the same function values for every x except when x = c. If two functions differ only at the value of c in their domain, then their limits as x approaches c are the same. This is because the value of a limit at a point is not dependent on the value of the function at that point.
Another technique is to rationalize the numerator or denominator.
Example 4: Evaluate each limit.
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In chapter 2, we learned at all evendegree power function have the same end behavior, and all odddegree power functions have the same end behavior summarized by the chart.
Also in chapter 2 we learned that the end behavior of a polynomial function is determined by the end behavior of the power function related to its highestpowered term.
Note: notating that the limit of ∞ or ∞ does not indicate that the limit exists, but instead describes the behavior of the function as increasing or decreasing without bound.
Also note: