Limit of x*cot(x)-1/x^2 as x->0

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Homework Help Overview

The discussion revolves around evaluating the limit of the expression x*cot(x) - 1/x^2 as x approaches 0, which presents an indeterminate form.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of L'Hôpital's rule and express concerns about its effectiveness. There are suggestions to rearrange the expression and consider power series expansions for sine and cosine functions.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to tackle the limit. Some have offered guidance on potential methods, such as using power series expansions, while others are questioning their initial assumptions and the effectiveness of their current strategies.

Contextual Notes

There is a noted indeterminacy in the limit, and participants are considering the implications of this in their approaches. The original poster expresses a desire for clarity in recognizing simplifications.

tsuwal
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Homework Statement


limit x*cot(x)-1/x^2
x->0



Homework Equations


lim x*cot(x)=1
x->0




The Attempt at a Solution


it's an indetermination but L'hopital rule doesn't help very much..
 
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tsuwal said:

Homework Statement


limit x*cot(x)-1/x^2
x->0



Homework Equations


lim x*cot(x)=1
x->0




The Attempt at a Solution


it's an indetermination but L'hopital rule doesn't help very much..

Sometimes l'Hopital works better if you try rearranging things. Substitute cot(x)=cos(x)/sin(x). Multiply numerator and denominator by sin(x) and try again.
 
tsuwal said:
limit x*cot(x)-1/x^2
x->0
I assume you mean limit (x*cot(x)-1)/x2 as x->0.
The indeterminacy simply means you've not gone far enough in the expansion of the functions as power series. What expansions do you know for tan x, or failing that, for sin x and cos x?
 
thanks Dick, i wish i could see the those simplifications right away!
 

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