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taylor polynomial math help
HalberdBlue
Registered User regular
Registered User regular
Quick math question that I can't find the answer to because I didn't write it down for some reason and its not in my book:
If I have an equation f(x)=g(x)h(x) and to find the Pn(x) of f(x) I find the Pn(x) of g(x) and the Pn(x) of h(x) and multiply them together, how are they multiplied? Is it using the FOIL method? Is it multiplying the nth term of f(x) by the nth term of g(x) and so on? And which "number" term is each term (needed if for example I need to find P4(x) and so would stop after the "4th" term). Thanks
EDIT: OK, finally found my notes on this. It doesn't really help though; its not what I thought. In this example, f(x) = x and g(x) = cosx^2, and so f(x)'s Pn(x) is just x. And its just multiplied by all of Pn(x) of g(x), so I'm guessing this uses the FOIL method then? Because in that case this is still a huge pain in the ass.
If I have an equation f(x)=g(x)h(x) and to find the Pn(x) of f(x) I find the Pn(x) of g(x) and the Pn(x) of h(x) and multiply them together, how are they multiplied? Is it using the FOIL method? Is it multiplying the nth term of f(x) by the nth term of g(x) and so on? And which "number" term is each term (needed if for example I need to find P4(x) and so would stop after the "4th" term). Thanks
EDIT: OK, finally found my notes on this. It doesn't really help though; its not what I thought. In this example, f(x) = x and g(x) = cosx^2, and so f(x)'s Pn(x) is just x. And its just multiplied by all of Pn(x) of g(x), so I'm guessing this uses the FOIL method then? Because in that case this is still a huge pain in the ass.
HalberdBlue on
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Actually, while you normally would have to foil and find the first few non-zero terms of the resulting series, in this case your g[x] has a simple expansion of x and all you'll have to do is distribute x into the expansion of you h[x], cos[x^2].
Something like: x*[1-x^4/2!+x^8/4!-...]==x-x^5/2!+x^8/4!-...==some kind of nth term expression, you can do that if you have to.
I think I was too, but the net result of doing the product rule and all that is the property you're using
In general it doesn't have to simplify to something pretty, though if you're expected to simplify it there'll probably be some pattern you can exploit and, as the other poster said, get some type of nth term expression