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

Thread starter johnnyICON
Start date Oct 12, 2004
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Limit

AI Thread Summary

To evaluate the limit of sin(x)/sqrt(x) as x approaches 0, it is noted that sin(x) approaches x, leading to the expression x/sqrt(x), which simplifies to sqrt(x). Additionally, the limit of sin(x)/x approaches 1, allowing the expression to be rewritten as (sin(x)/x) * sqrt(x). As x approaches 0, sqrt(x) approaches 0, thus the overall limit is 0. This method effectively demonstrates the evaluation of the limit.

Oct 12, 2004

johnnyICON

Limits! help!

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

Evaluate: \lim_{x \to 0} \frac{\sin{x}}{\sqrt{x}}

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Oct 12, 2004

Leong

When x approaches 0, sin x approaches x. so you get
\frac{x}{\sqrt{x}}=\sqrt{x}

Oct 12, 2004

Galileo

Science Advisor

Homework Helper

Or remember that \frac{sinx}{x} goes to 1. Then write
\frac{\sin{x}}{\sqrt{x}}=\frac{\sin{x}}{x}\sqrt{x}

Oct 12, 2004

johnnyICON

awesome, thanks!

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