Calculating the Limit: $\lim_{x\to0}\frac{\sin x-x }{x^3}$

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Homework Help Overview

The discussion revolves around calculating the limit of the expression $\lim_{x\to0}\frac{\sin x-x }{x^3}$, which falls under the subject area of calculus, specifically limits and series expansions.

Discussion Character

  • Exploratory, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants explore different methods to evaluate the limit, including the application of L'Hopital's Rule and the power series expansion for sine. There is also a discussion about the indeterminate form encountered in the limit.

Discussion Status

The discussion is ongoing, with participants sharing various approaches and questioning the effectiveness of their attempts. Some guidance has been offered regarding potential methods to resolve the limit, but no consensus has been reached.

Contextual Notes

Participants are grappling with the indeterminate form of the limit and the implications of applying different mathematical techniques, such as L'Hopital's Rule and series expansions.

MHD93
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Hi


Find the limit:
[tex]\lim_{x\to0}\frac{\sin x-x }{x^3}[/tex]
 
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Mohammad_93 said:
Hi


Find the limit:
[tex]\lim_{x\to0}\frac{\sin x-x }{x^3}[/tex]
What have you tried?
 
lim[x->0] (sinx - x)/x^3 = lim [x->0] sinx/x3 - 1/x2
but it's infinity - infinity!
 
So that didn't do you any good.

Do you know about L'Hopital's Rule?
 
Or the power series for sin x?
 

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