What is the Taylor Polynomial for Arcsin x at a = 0 and n = 3?

Click For Summary

Homework Help Overview

The discussion revolves around finding the Taylor polynomial for the function arcsin x at a = 0, specifically for n = 3. Participants are exploring the process of deriving the polynomial and the complexities involved with the arcsine function compared to the sine function.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need to evaluate the function and its derivatives at a specific point, questioning how to handle the derivatives of arcsin compared to sine. There is also a mention of the difficulty in taking the derivative of arcsin.

Discussion Status

The conversation indicates that some participants have made progress in understanding the problem, with one expressing that they have resolved their confusion. However, there is no explicit consensus on the approach or final outcome.

Contextual Notes

There is an implication that participants may be constrained by their understanding of derivatives, particularly for the arcsine function, which is noted to be more challenging than that of sine.

vigintitres
Messages
25
Reaction score
0

Homework Statement



Find the Taylor polynomial T_n(x) for the function arcsin x at a = 0, n = 3

Homework Equations



Well, I understand the Taylor poly. for sine, but how do i get arcsine?
 
Physics news on Phys.org
Put f(x)=arcsin(x)
find f(0),f'(0) and so on and just put it into the formula.
 
Okay, is the problem that you don't know how to take the derivative or arcsin? Because if you can do that then the rest of the problem should be just like finding the taylor polynomial of sine.

I tried the problem out and the only thing that's different then the sine curve problem is that taking the derivative of arcsin is considerably harder.
 
Last edited:
thanks all, got it...
 

Similar threads

Taylor polynomial, approximative solution of this equation
  • · Replies 3 ·
Replies
3
Views
1K
Show that the Taylor series for this Lagrangian is the following...
  • · Replies 4 ·
Replies
4
Views
2K
What is the Taylor expansion of x/sin(ax)?
  • · Replies 5 ·
Replies
5
Views
3K
Limit of the remainder of Taylor polynomial of composite functions
  • · Replies 2 ·
Replies
2
Views
2K
Lagrange error bound inequality for Taylor series of arctan(x)
  • · Replies 1 ·
Replies
1
Views
3K
Link between Z-transform and Taylor series expansion
  • · Replies 2 ·
Replies
2
Views
2K
Bounds of the remainder of a Taylor series
  • · Replies 27 ·
Replies
27
Views
4K
Evaluate the Taylor series and find the error at a given point
  • · Replies 6 ·
Replies
6
Views
3K
How should I show that this root is given approximately by this?
  • · Replies 2 ·
Replies
2
Views
2K
Basic Taylor Polynomial Question involving e^(-x)^2
  • · Replies 9 ·
Replies
9
Views
2K