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how to represent certain types of functions as sums of power series
MACLAURIN SERIES how to represent certain types of functions as sums of 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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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-131
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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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Example: MACLAURIN SERIES
Important Maclaurin Series and Their Radii of Convergence Example: Find Maclaurin series
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MACLAURIN SERIES TERM-122
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MACLAURIN SERIES TERM-082
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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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