- #1

StephenD420

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I am a senior physics undergraduate student. I have wondered about the Taylor Expansion for a few years now and just have never bothered to ask. But I will now:

I know the Taylor Expansion goes like:

f(a) + [itex]\frac{f'(a)}{1!}[/itex]*(x-a) + [itex]\frac{f''(a)}{2!}[/itex]*(x-a)[itex]^{2}[/itex] + [itex]\frac{f'''(a)}{3!}[/itex]*(x-a)[itex]^{3}[/itex] + ...

which is the same as [itex]\sum[/itex] [itex]\frac{f^{n}(a)}{n!}[/itex]*(x-a)[itex]^{n}[/itex]

but how do you know when you use this to approximate a formula? Any problem that my professors have given they have explicitly said to use a Taylor Expansion, but I know there has to be a rule of thumb when to use the Taylor Expansion to approximate a formula.

Any ideas?

Thanks much.

Stephen