Solving Homework Equations: Taylor Series & Beyond

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SUMMARY

The discussion focuses on solving homework equations related to Taylor series and potential energy in physics. The user derived a force equation, F(r) = α(ke²)((-r₀/r²)+(r₀n/rⁿ⁺¹)), indicating that the force is the negative derivative of potential energy. The user is uncertain about applying the Taylor expansion for part b, specifically whether to use the derived equation or its derivative. Clarification is sought regarding the appearance of (n-1) and the n term in the exponent of the expected answer.

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  • Understanding of Taylor series and its applications in physics.
  • Knowledge of calculus, specifically derivatives and their physical interpretations.
  • Familiarity with potential energy concepts in classical mechanics.
  • Basic algebra skills for manipulating equations and exponents.
NEXT STEPS
  • Study the application of Taylor series in physics problems.
  • Review calculus concepts related to derivatives and their physical significance.
  • Explore potential energy equations and their derivatives in classical mechanics.
  • Practice solving problems involving Taylor expansions and their applications.
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Students in physics or engineering courses, particularly those tackling homework involving Taylor series and potential energy calculations.

cjw21
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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)= \alpha(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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sorry, double post
 

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