Question from LeDuc

Forum for the GRE subject test in mathematics.
mk
Posts: 13
Joined: Fri May 22, 2009 1:14 am

Question from LeDuc

Postby mk » Thu Aug 27, 2009 1:34 pm

The question is: If f(x) = e^x is expanded in its Taylor series, what is the minimum number of terms that must be used to ensure that the resulting polynomial will approximate e^(1/5) to within 10^-6. They say that the answer is 5.

I agree with their reasoning that (f^6(c)(1/5)^6/6!) < 10^-6 and that 5 doesnt work there. So we need to expand the Taylo series until it includes x^5, making it 1+x+x^2/2+x^3/3!+x^4/4!+x^5/5!. But that polynomial has 6 terms, so the minimum number of terms should be 6. I understand that in his notation this polynomial is P5, but P5 has 6 terms! Have I gotten something wrong here?

Nameless
Posts: 128
Joined: Sun Aug 31, 2008 4:42 pm

Re: Question from LeDuc

Postby Nameless » Thu Sep 03, 2009 10:23 pm

I guess for this question, it is asking about the degree of the polynomial rather than the number of terms of the polynomial !




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