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anonymous
 one year ago
How to find the limit of sin(x)/x as x approaches zero?
For example, the problem is sin (2x)/ 8x, how to find the limit as x approaches to zero?
anonymous
 one year ago
How to find the limit of sin(x)/x as x approaches zero? For example, the problem is sin (2x)/ 8x, how to find the limit as x approaches to zero?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0will it be 1/4 since the limit of sin(x)/x is equal to 1?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We know that \[\lim_{x \rightarrow 0} \frac{\sin x}{x} = 1\] Looking at the given problem \[\lim_{x \rightarrow 0} \frac{\sin 2x}{8x} \] In order to get the problem to look like the form sin x / x, we need the denominator of the fraction to equal 2x. Setting the bottom to 2x, the limit looks like this: \[n \ \lim_{x \rightarrow 0} \frac{\sin 2x}{2x} \] In order for the above to be true, we would have to multiply the limit by some number \(n\). That's what you have to find.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, it works out to be 1/4.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ah okay thanks! one more question, why is it that \(\lim_{x \rightarrow 0} \frac{\sin x}{x} = 1\) ? Is there a proof that it is equal to 1?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just know about it but I never learned the reason behind it
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