1. TAYLOR SERIES

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

3. TAYLOR SERIES
TERM-131

4. TAYLOR SERIES
TERM-101

5. TAYLOR SERIES
TERM-082

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

7. 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

8. 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 :

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

10. The Binomial Series

11. 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

12. The Binomial Series
DEF:
NOTE:
Example:
Example:

13. The Binomial Series
binomial series.

14. TERM-101 The Binomial Series Do the calculation slowly

15. The Binomial Series
TERM-122
binomial series.

16. The Binomial Series
TERM-092
binomial series.

17. 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)

18. Applications of Taylor Series
TERM-111

19. Applications of Taylor Series
TERM-102

20. TAYLOR AND MACLAURIN
TERM-092

21. TAYLOR AND MACLAURIN
TERM-081