I'm trying to find the first five terms of a Maclaurin series using division.
Is there possibly a shorter way because every time I try to do it for $\frac{\sin x}{e^x}$
I get the wrong answer: $x-2x^3/3+\cdots$
I don't really like polynomial long division.
This is how I set it up:
x - x^3/3! + x^5/5! - x^7/7! ÷ 1 + x + x^2/2! + x^3/3! + x^4/4!
I'm still getting the same answer.