Power series

  • Thread starter psyklon
  • Start date
  • #1
10
0

Homework Statement


The problem I'm attempting to solve asks you to evaluate the function at a given point. In this case:

ln(x + sqrt[1+x2] ) - sin(x)
@ x = .001


Homework Equations


sin(x) = x - (x3/3!) + (x5/5!) - (x7/7!) + ...
AND
ln(1 + x) = x - (x2/2) + (x3/3) - (x4/4) + ...


The Attempt at a Solution


I know I'm supposed to substitute in the power series expansions, but I'm not sure how to begin modifying the second expansion to suit my needs in solving the problem. Can anyone point me in the right direction?
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,223
31
Since x is small, you can approximate sin(x) as just x, you can do the same with the other functions.
 

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