21122 Final Review - 21-122 Integration Dierential...

This preview shows page 1 out of 1 page.

21-122Integration, Differential Equations, and ApproximationD. HandronFinal Exam ReviewFall 20111. Determine the interval of convergence and the radius of convergence for the power seriesn=1(-1)n(2x+3)nnln(n).2.(a) Find the Taylor series forf(x) = ln(x) aroundx= 2.(b) Find the Taylor series forg(x) = (x-2)2ln(x) aroundx= 2.3. Recall that11-x=n=0xnfor|x|<1.(a) Use this MacLauren series to find a Taylor series for-ln(1-x).(b) Find the first five terms in the MacLauren series for-ln(1-x)1-x.4. Recall thatex=summationdisplayn=1xnn!11-x=summationdisplayn=1xcos(x) =summationdisplayn=1(-1)nx2n(2n)!(a) Expressintegraltextcos(x2)dxas a power series.(b) What is the radius of convergence for this power series?(c) Find the fourth degree Taylor polynomial for

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture