- #1
GreenPrint
- 1,196
- 0
Hi,
If I'm given something like this for a problem,
Approximate the given quantities using Taylor polynomials with n=3
sqrt(101)
how do I know what I should set f(x) equal to? I could set it to many different things, sqrt(x), sqrt(x+100), sqrt(x+50). My answer would be very different depending on what I set f(x) equal to. Like if I used f(x)=sqrt(x) and I centered it at x=0 I'm going to get zero for the derivatives, f(x)' = 1/(2sqrt(x)), and this is going to make p3(x) a different function had I used f(x)=sqrt(x+100) instead.
So I take it I can use what ever I want for f(x) on such a problem and my grader will just have to check everyone's paper with a fine tooth comb because people you can use a infinite amount of functions to set f(x) equal to?
If I'm given something like this for a problem,
Approximate the given quantities using Taylor polynomials with n=3
sqrt(101)
how do I know what I should set f(x) equal to? I could set it to many different things, sqrt(x), sqrt(x+100), sqrt(x+50). My answer would be very different depending on what I set f(x) equal to. Like if I used f(x)=sqrt(x) and I centered it at x=0 I'm going to get zero for the derivatives, f(x)' = 1/(2sqrt(x)), and this is going to make p3(x) a different function had I used f(x)=sqrt(x+100) instead.
So I take it I can use what ever I want for f(x) on such a problem and my grader will just have to check everyone's paper with a fine tooth comb because people you can use a infinite amount of functions to set f(x) equal to?