CK-12-Calculus

8.7. Taylor and Maclaurin Series http://www.ck12.org Then f 1 ′(x) =    ( 2 x^3 )·e−x (^12) x 6 = 0 0 x= 0 It can be verifi ...

http://www.ck12.org Chapter 8. Infinite Series f′(x) =^12 ( 1 +x)−^12 ,f′′(x) =^12 ( −^12 ) ( 1 +x)−^32 =−^14 ( 1 +x)−^32 , f′′′ ...

8.7. Taylor and Maclaurin Series http://www.ck12.org by dividing into sum of odd and even indices. So cosx+isinx=∑∞m= 0 (− 1 )m( ...

http://www.ck12.org Chapter 8. Infinite Series So if|x|< 1 ,√ 1 +x=∑∞k= 1 (k^21 )xk= 1 +∑∞k= 1 ( 2 − 21 k−)k 1 −k^1 !((^2 k−k ...

8.7. Taylor and Maclaurin Series http://www.ck12.org This pattern repeats and limn→∞Rn(x) =0 can be checked as in the casex 0 =0 ...

http://www.ck12.org Chapter 8. Infinite Series ex x= e·eu 1 +u=e· 1 1 +u ∞ n∑= 0 (u)n n! =e( 1 −u+u^2 −u^3 +...) ( 1 +u+u 2 2!+ ...

8.7. Taylor and Maclaurin Series http://www.ck12.org Multimedia Links For video presentations on the Taylor and Maclaurin Series ...

http://www.ck12.org Chapter 8. Infinite Series 8.8 Calculations with Series Binomial Series We have learned the Binomial Theorem ...

8.8. Calculations with Series http://www.ck12.org Solution. We need to compute the Binomial coefficients forr=−m(and will replac ...

http://www.ck12.org Chapter 8. Infinite Series Since 1.1 is close toπ 3 , we would try to find a Taylor Series of sinxatx 0 =π 3 ...

8.8. Calculations with Series http://www.ck12.org ex x = e·eu 1 +u=e· 1 1 +u ∞ n∑= 0 (u)n n! =e( 1 −u+u^2 −u^3 +...) ( 1 +u+u 2 ...

http://www.ck12.org Chapter 8. Infinite Series Texas Instruments Resources In the CK-12 Texas Instruments Calculus FlexBook® res ...