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how to represent certain types of functions as a power series
MACLAURIN SERIES how to represent certain types of functions as a power series You might wonder why we would ever want to express a known function as a sum of infinitely many terms. Integration. (Easy to integrate polynomials) Finding limit Finding a sum of a series (not only geometric, telescoping) How does the calculator find values of sine (or cosine or tangent)?
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Maclaurin series ( center is 0 )
Example: Maclaurin series ( center is 0 ) Example: Find Maclaurin series
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MACLAURIN SERIES Example: Find Maclaurin series Example: Find Maclaurin series Example: Find Maclaurin series Example: Find Maclaurin series Example: Find Maclaurin series
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MACLAURIN SERIES Important Maclaurin Series and Their Radii of Convergence MEMORIZE: ** Students are required to know the series listed in Table 10.1, P. 620 How to memorize them
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Important Maclaurin Series and Their Radii of Convergence
MEMORIZE: ** Students are required to know the series listed in Table 10.1, P. 620 Denominator is n! even, odd Denominator is n odd
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Maclaurin series ( center is 0 )
How to find a Maclaurin Series of a function Use the formula Use the known functions 1) Replace each x 2) Diff 3) integrate 3) Find a product between two
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MACLAURIN SERIES TERM-081
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MACLAURIN SERIES TERM-091
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MACLAURIN SERIES TERM-101
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MACLAURIN SERIES TERM-082
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MACLAURIN SERIES TERM-102
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MACLAURIN SERIES TERM-091
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Find the sum of a series using Maclaurin Series
Geometric + Telescoping
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TAYLOR AND MACLAURIN Example: Find the sum of the series
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MACLAURIN SERIES TERM-102
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MACLAURIN SERIES TERM-082
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MACLAURIN SERIES TERM-141
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MACLAURIN SERIES TERM-131
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MACLAURIN SERIES TERM-132
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MACLAURIN SERIES Example: Find the sum Leibniz’s formula:
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Important Maclaurin Series and Their Radii of Convergence
MEMORIZE: ** Students are required to know the series listed in Table 10.1, P. 620 Denominator is n! even, odd Denominator is n odd MAC
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MACLAURIN SERIES Example: Find Maclaurin series
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Integration using Maclaurin Series
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MACLAURIN SERIES TERM-122
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MACLAURIN SERIES TERM-141
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Important Maclaurin Series and Their Radii of Convergence
MEMORIZE: ** Students are required to know the series listed in Table 10.1, P. 620 Denominator is n! even, odd Denominator is n odd
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