TAYLOR SERIES

TAYLOR SERIES Maclaurin series ( center is 0 ) Taylor series ( center is a )

TAYLOR SERIES TERM-131

TAYLOR SERIES TERM-101

TAYLOR SERIES TERM-082

TAYLOR SERIES Taylor series ( center is a ) DEF: Taylor polynomial of order n

TAYLOR SERIES The Taylor polynomial of order 3 generated by the function f(x)=ln(3+x) at a=1 is: TERM-102 DEF: Taylor polynomial of order n

Taylor series ( center is a ) Taylor polynomial of order n Remainder Taylor Series Taylor’s Inequality Remainder consist of infinite terms IF THEN REMARK: Observe that :

IF THEN IF THEN TAYLOR SERIES Taylor’s Inequality Taylor’s Inequality (center is zero) IF THEN

The Binomial Series

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

The Binomial Series DEF: NOTE: Example: Example:

The Binomial Series binomial series.

TERM-101 The Binomial Series Do the calculation slowly

The Binomial Series TERM-122 binomial series.

The Binomial Series TERM-092 binomial series.

1) Integration. (Easy to integrate polynomials) Applications of Taylor Series 1) Integration. (Easy to integrate polynomials) 2) Finding limit 3) Finding a sum of a series (not only geometric, telescoping)

Applications of Taylor Series TERM-111

Applications of Taylor Series TERM-102

TAYLOR AND MACLAURIN TERM-092

TAYLOR AND MACLAURIN TERM-081