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)?
Maclaurin series ( center is 0 ) Example: Maclaurin series ( center is 0 ) Example: Find Maclaurin series
MACLAURIN SERIES Example: Find Maclaurin series Example: Find Maclaurin series Example: Find Maclaurin series Example: Find Maclaurin series Example: Find Maclaurin series
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
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
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
MACLAURIN SERIES TERM-081
MACLAURIN SERIES TERM-091
MACLAURIN SERIES TERM-101
MACLAURIN SERIES TERM-082
MACLAURIN SERIES TERM-102
MACLAURIN SERIES TERM-091
Find the sum of a series using Maclaurin Series Geometric + Telescoping
TAYLOR AND MACLAURIN Example: Find the sum of the series
MACLAURIN SERIES TERM-102
MACLAURIN SERIES TERM-082
MACLAURIN SERIES TERM-141
MACLAURIN SERIES TERM-131
MACLAURIN SERIES TERM-132
MACLAURIN SERIES Example: Find the sum Leibniz’s formula:
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
MACLAURIN SERIES Example: Find Maclaurin series
Integration using Maclaurin Series
MACLAURIN SERIES TERM-122
MACLAURIN SERIES TERM-141
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