This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: x on a longer and longer interval about 0. To be extreme about it, lets skip ahead to T 25 ( x ): T 25 ( x ) = xx 3 3! + x 5 5!x 7 7! + x 9 9!x 11 11! + x 13 13!x 15 15! + x 17 17!x 19 19! + x 21 21!x 23 23! + x 25 25! . Figure 6. sin x and T 25 ( x ) To the naked eye, T 25 ( x ) lies right on top of sin x for three periods of sin x ! Another way to think of this would be to consider the remainder functions R n ( x ) = sin( x )T n ( x ). Lets graph them all on one set of axes; notice how each one seems to lie on the xaxis for longer than the previous ones (i.e., that R n ( x ) 0 for all x ): 4 Figure 7. Plots (from inside out) of R 1 ( x ) (solid), R 3 ( x ) (dotted), R 5 ( x ) (dashed), R 7 ( x ) (dotdashed) and R 25 ( x ) (solid again)...
View Full
Document
 Spring '08
 REMPE
 Taylor Series

Click to edit the document details