Limit of f(x) as x tends to 0 for f(x)=[sinx]/[x^2]

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Homework Help Overview

The discussion revolves around the limit of the function f(x) = [sin(x)]/[x^2] as x approaches 0, specifically questioning whether a limit exists in this context.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the behavior of the function as x approaches 0, with one noting the indeterminate form 0/0 and suggesting the need for further analysis. Others reference known limits and potential methods, such as l'Hôpital's rule, to evaluate the limit.

Discussion Status

The discussion is active, with participants providing insights into the nature of the limit and referencing relevant mathematical concepts. There is no explicit consensus, but several lines of reasoning are being explored.

Contextual Notes

Participants are navigating the implications of the indeterminate form and considering established limits related to sine functions, indicating a need for deeper exploration of the problem.

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Homework Statement



Does f(x) tend to a limit as x tends to 0?

Homework Equations



f(x)=[sinx]/[x^2]

The Attempt at a Solution



Well i sinx would tend to zero and so would x^2, so would the limit just be zero?
 
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No, 0/0 is an indeterminant form. It means you have to work harder. Do you know the limit of sin(x)/x? Do you know l'Hopital's rule?
 
Do you know that:
[tex]\lim_{x \rightarrow 0}\frac{sinx}{x}=1[/tex]

?
 
[tex]\frac{sin(x)}{x^2}= \left(\frac{sin(x)}{x}\right)\left(\frac{1}{x}\right)[/tex]
 

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