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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?

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  1. anonymous
    • one year ago
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    will it be 1/4 since the limit of sin(x)/x is equal to 1?

  2. displayerror
    • one year ago
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    We 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.

  3. displayerror
    • one year ago
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    Yeah, it works out to be 1/4.

  4. anonymous
    • one year ago
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    ah 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?

  5. anonymous
    • one year ago
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    I just know about it but I never learned the reason behind it

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