Solving Homework Equations: Taylor Series & Beyond

In summary, the conversation is about a homework problem that involves finding the force and potential equations using the Taylor series expansion. The solution for part a involves using the negative derivative of potential, while the solution for part b involves using a Taylor expansion. The question asks for clarification on which equation to use and how to get certain terms in the answer.
  • #1
cjw21
6
0

Homework Statement



rATBV.jpg


Homework Equations



All should be there, except taylor series, which is found here:

http://mathworld.wolfram.com/TaylorSeries.html

The Attempt at a Solution



For part a, I got:

F(r)= [itex]\alpha[/itex](ke2)((-r0/r2)+(r0n/rn+1))

since force is the negative derivative of potential.

I'm pretty sure the answer to part b will involve a taylor expansion, but I'm not sure if the f(x) I use will be the equation I found in part a, or the derivative of the equation I found in part a. Additionally, I'm not sure how, in the answer we're supposed to get that's listed in the problem, they got (n-1) and the n term in the second part out of the exponent.

Thanks for any help!
 
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  • #2


sorry, double post
 

FAQ: Solving Homework Equations: Taylor Series & Beyond

What is a Taylor series and why is it important in solving homework equations?

A Taylor series is a mathematical representation of a function as an infinite sum of terms. It is important in solving homework equations because it allows for the approximation of a function with a polynomial, making it easier to find solutions to complex equations.

What are some common techniques for solving equations using Taylor series?

Some common techniques for solving equations using Taylor series include finding the coefficients of the series, using the remainder term to estimate error, and using the series to find derivatives and integrals of functions.

Can Taylor series be used for non-polynomial functions?

Yes, Taylor series can be used for non-polynomial functions. However, the resulting series may not converge or may only converge for a limited range of values.

What is the difference between a Maclaurin series and a Taylor series?

A Maclaurin series is a special case of a Taylor series where the series is centered at x=0. This means that the power series only includes non-negative integer powers of x. A Taylor series can be centered at any point on the x-axis.

How do I know if a Taylor series is an appropriate method for solving a homework equation?

A Taylor series is typically used for solving equations where the function and its derivatives are known at a specific point. It is also useful for approximating complex functions with a polynomial. If these conditions are met, then a Taylor series may be an appropriate method for solving a homework equation.

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