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, let’s 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 ). Let’s 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, Sin

Click to edit the document details