Author 
Topic 

Francneto
Junior Member
Angola
3 Posts 
Posted  09/11/2007 : 07:09:32

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



Subhotosh Khan
Advanced Member
USA
9117 Posts 
Posted  09/11/2007 : 07:21:40

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. 


royhaas
Moderator
USA
3059 Posts 
Posted  09/13/2007 : 17:21:35

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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