if f(x) approximate g(x) within 1/3000 for 10

Question

if f(x) approximate g(x) within 1/3000 for 10<x<12 then integral f(x)dx from 10 to 12 approximates integral g(x)dx from 10 to 12 to how many accurate decimals

anonymous · Answer

you always come up with the damndest questions
but lets say $f(x)=0$ and $g(x)=\frac{1}{3000}$ which is as far as it can be
then $$\int_{10}^{12}f(x)dx=0$$ and
$$\int_{10}^{12}\frac{1}{3000}=\frac{2}{3000}$$

anonymous · Answer

a more sophisticated way to answer would be to say that 
$$\int f -\int g =\int (f-g)\leq \int \frac{1}{3000}=\frac{2}{3000}$$

anonymous · Answer

an even more sophisticated way to answer would be to use absolute values, but enough already

anonymous · Answer

did you get an answer to that series with the squares?  that bedevilled me for a while

anonymous · Answer

the series with squares? which one..i don't even remember..lol

anonymous · Answer

$$x+2^2x^2+3^2x^3+4^2x^4+...$$

anonymous · Answer

or maybe it started with 1, i don't remember but i could not figure out how to get that square there

anonymous · Answer

i think the series is e^x expansion and minus first two term....lol right?

anonymous · Answer

yeah right
your questions vary from more or less immediately obvious to wtf  with very little in between

anonymous · Answer

maybe a bi-polar professor?

anonymous · Answer

i don't know ..i'm taking an online calculus...it's really frustrate me