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 Pre-Calculus and Calculus
 Calculus - Taylor Series
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Francneto
Junior Member

Angola
3 Posts

Posted - 09/11/2007 :  07:09:32  Show Profile
Please help me! I was trying to solve this problem but the more I try the more confused I get. I'm even shy to show what I have tried. The problem are the following:

1. Let f(x)=tan^-1(x)

a) Obtain the 3rd degree Taylor polynomial P3(x) and the Taylor remainder R3(x) about c=1 for the given function.

b) Use P3(x) to estimate tan^-1(0.7) and use R3(x) to estimate the error in the approximation.

2. Obtain the reduction formula for cos^n[x]dx
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Subhotosh Khan
Advanced Member

USA
9117 Posts

Posted - 09/11/2007 :  07:21:40  Show Profile
quote:
Originally posted by Francneto

Please help me! I was trying to solve this problem but the more I try the more confused I get. I'm even shy to show what I have tried. The problem are the following:

1. Let f(x)=tan^-1(x)

a) Obtain the 3rd degree Taylor polynomial P3(x) and the Taylor remainder R3(x) about c=1 for the given function.

b) Use P3(x) to estimate tan^-1(0.7) and use R3(x) to estimate the error in the approximation.

2. Obtain the reduction formula for cos^n[x]dx



Please show us what you have tried - so that we know where to start.
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royhaas
Moderator

USA
3059 Posts

Posted - 09/13/2007 :  17:21:35  Show Profile
Do not use the "Report a Post" function to show your work. Just post a reply.

If you are expanding the arctan function around c=1, then your first term is arctan(1). Do not factor into complex numbers. Compute the derivatives and evaluate at x=1. In other words, use the definition of a Taylor polynomial.
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