Max Errors:
Error(T_(N))<=(K_(2)(b-a)^(3))/(12N^(2)),Error(M_(N))<=(K_(2)(b-a)^(3))/(24N^(2)),Error(S_(N))<=(K_(4)(b-a)^(5))/(180N^(4))
Find the maximum possible error associated in using
T_(10)
to approximate
\int_0^1 e^(-4x)dx
. Find the value of N for which
S_(N)
approximates
\int_0^((\pi )/(2)) sin(2x)dx
with an error of at most 0.001 .