Using Lagrange Error Bound

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Homework Statement



Im supposed to use the lagrange error bound to find a bound for the error when approximating ln(1.5) with a third degree taylor polynomial about x=0, where f(x)=ln(1+x)



Homework Equations



Lagrange error bound

m/(n+1)! abs(x-a)^n+1, m=f(n+1)(c)



The Attempt at a Solution



The error bound is basically the next term in the series (correct?) So if im looking for a bound on a third degree taylor polynomial i would have 4 factorial in the denominator. And I would let m=ln(1.5) since that is the greatest possible value on the interval.

So I would have something that looks like this:

Error < ln(1.5)/4! * abs(.5)^4 =.001055

Answer in my book says it should be .0156. So where am I going wrong? Thanks for the help.
 

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