How Do You Evaluate the Limit of sin(x)/sqrt(x) as x Approaches 0?

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Homework Help Overview

The discussion revolves around evaluating the limit of the function sin(x)/sqrt(x) as x approaches 0, which falls under the topic of limits in calculus.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore different approaches to evaluate the limit, including the behavior of sin(x) as x approaches 0 and the relationship between sin(x) and x. Some suggest rewriting the expression to facilitate evaluation.

Discussion Status

Participants are sharing insights and methods for approaching the limit, with some guidance provided on manipulating the expression. There is an ongoing exploration of different interpretations and approaches without a clear consensus yet.

Contextual Notes

No specific constraints or missing information have been noted in the discussion.

johnnyICON
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Limits! help!

I have this question that I am not too sure of how to do, can anyone help me?

Evaluate: [itex]\lim_{x \to 0} \frac{\sin{x}}{\sqrt{x}}[/itex]
 
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When x approaches 0, sin x approaches x. so you get
[tex]\frac{x}{\sqrt{x}}=\sqrt{x}[/tex]
 
Or remember that [itex]\frac{sinx}{x}[/itex] goes to 1. Then write
[tex]\frac{\sin{x}}{\sqrt{x}}=\frac{\sin{x}}{x}\sqrt{x}[/tex]
 
awesome, thanks! :smile:
 

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