i keep looking at this problem and don't understand how to eliminate terms and find a value for n ... any help would be thankful
Consider the functions f(x)=e^x and f(x)=sin(x) (for this problem assume familiar facts about exponentials, sines and cosines) Let Pn be the nth Taylor polynomial for f based at s=0. The error is Rn(x)=f(x) -Pn(x).
first part is:
a.) Determine a value of n such that |Rn(3)| <= 0.001. Crude upper estimates are fine and we are allowed e<=3.
i was given a corollary where |Rn(x)|<= (K/(n+1)!)*|x-s|^(n+1) ;K is a positive real
any help on what i should start thinking about ... and how to approach this would be grateful