C cheffy Junior Member Joined Jan 10, 2007 Messages 73 Apr 14, 2007 #1 The estimate \(\displaystyle \ \sqrt {1 + x} = 1 + \frac{x}{2} \\) is used when x is small. Estimate the error when |x|<0.1 I know it has something to do with |-(x^2)/8|, at least I think, but I don't know what to do from here. Thanks!
The estimate \(\displaystyle \ \sqrt {1 + x} = 1 + \frac{x}{2} \\) is used when x is small. Estimate the error when |x|<0.1 I know it has something to do with |-(x^2)/8|, at least I think, but I don't know what to do from here. Thanks!
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,203 Apr 15, 2007 #2 Try the Taylor series: \(\displaystyle \L\\\sqrt{1+x}=1+\frac{x^{2}}{2}-\frac{x^{2}}{8}+...........\) \(\displaystyle \L\\1+\frac{1}{x}=1+\frac{x}{2}\)
Try the Taylor series: \(\displaystyle \L\\\sqrt{1+x}=1+\frac{x^{2}}{2}-\frac{x^{2}}{8}+...........\) \(\displaystyle \L\\1+\frac{1}{x}=1+\frac{x}{2}\)
C cheffy Junior Member Joined Jan 10, 2007 Messages 73 Apr 15, 2007 #3 What am I supposed to do with that? I don't understand how you got the second line.
