Unit 12. Unit 12: Sequences and Series Vocabulary.
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Transcript of Unit 12. Unit 12: Sequences and Series Vocabulary.
![Page 1: Unit 12. Unit 12: Sequences and Series Vocabulary.](https://reader031.fdocuments.in/reader031/viewer/2022031821/56649c9d5503460f9495caa2/html5/thumbnails/1.jpg)
Sequences and SeriesUnit 12
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Arithmetic and Geometric SequencesUnit 12: Sequences and Series
![Page 3: Unit 12. Unit 12: Sequences and Series Vocabulary.](https://reader031.fdocuments.in/reader031/viewer/2022031821/56649c9d5503460f9495caa2/html5/thumbnails/3.jpg)
Vocabulary
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Arithmetic Sequences
![Page 5: Unit 12. Unit 12: Sequences and Series Vocabulary.](https://reader031.fdocuments.in/reader031/viewer/2022031821/56649c9d5503460f9495caa2/html5/thumbnails/5.jpg)
Geometric Sequences
![Page 6: Unit 12. Unit 12: Sequences and Series Vocabulary.](https://reader031.fdocuments.in/reader031/viewer/2022031821/56649c9d5503460f9495caa2/html5/thumbnails/6.jpg)
SeriesUnit 12: Sequences and Series
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Series
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Sigma Notation
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Series Shortcuts
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Series Shortcuts
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Limits of FunctionsUnit 12: Sequences and Series
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Informal Definition of a LimitLet f be a function and c be a real number
such that f(x) is defined for all values of x near x=c.
Whenever x takes on values closer and closer but not equal to c (on both sides of c), the corresponding values of f(x) get very close to, and possibly equal, to the same real number L and the values of f(x) can be made arbitrarily close to L by taking values of x close enough to c, but not equal to c.
![Page 13: Unit 12. Unit 12: Sequences and Series Vocabulary.](https://reader031.fdocuments.in/reader031/viewer/2022031821/56649c9d5503460f9495caa2/html5/thumbnails/13.jpg)
Definition of a LimitThe limit of the function f(x) as x approaches c
is the number L.
This can be written as:
![Page 14: Unit 12. Unit 12: Sequences and Series Vocabulary.](https://reader031.fdocuments.in/reader031/viewer/2022031821/56649c9d5503460f9495caa2/html5/thumbnails/14.jpg)
ExamplesFind
Notice that
3
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ExamplesFind
Notice that undefined
1
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ExamplesFind
Notice that
∞
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When Limits Do Not ExistIf 𝑓(𝑥) approaches ∞ as x approaches c from
the right and 𝑓(𝑥) approaches −∞ as x approaches c from the left or 𝑓(𝑥) approaches −∞ as x approaches c from the right and 𝑓(𝑥) approaches ∞ as x approaches c from the left.
Find
Does Not Exist
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When Limits Do Not ExistIf approaches L as x approaches c from the
right and approaches M, with , as x approaches c from the left.
Find
Does Not Exist
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When Limits Do Not ExistIf 𝑓(𝑥) oscillates infinitely many times
between two numbers as x approaches c from either side.
Find
Does Not Exist
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Limits at InfinityLet be a function that is defined for all for
some number a if:as , and the values of can be made arbitrarily close
to L by taking large enough values of x,then the limit of as is L, which is written
(the limit of a function is a statement about the end behavior)
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ExamplesFind Find
+ 1
6
1
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ExamplesFind Find
0
0
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Infinite SeriesUnit 12: Sequences and Series
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Convergence of a Sequence
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Convergence of a Series
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Convergence of a Series