Establish an infinite series expansion for the function y=e^(-x)cos(x) from the known series expansions, include terms up to the sixth power.
The series expansions of e^x and cos(x).
The Attempt at a Solution
I am unsure of how many terms to multiply out to make the value accurate. I have tried the first four terms of e^(-x) multiplied by the first three of cos(x), then I dropped the x^7 term. This feels wrong. I have confidence that wolframalpha has the correct answer. How do I know what terms to keep/drop? I have: 1 -x +x^3/3 -x^4/12 -x^5/12 +x^6/12.