Limit of sin(3x)/x as x approaches 0 | Calculus 1 Exercises

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We show the limit of sin(3x)/x as x goes to 0 is equal to 3. To evaluate this trigonometric limit, we need to remember the limit of sin(x)/x with x approaching 0, which is a fundamental trigonometric limit equal to 1! If we remember this, we'll be able to solve the problem in short order. #Calculus1 #apcalculus

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WrathofMath
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Very clear and simple explanation. 2:58

EE-Spectrum
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so we can generally say

lim (x -> 0) [sin(cx) / x] = c
lim (x -> 0) [sin(x) / (cx)] = 1/c

am i right?

adi-tiny
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Is it because when you use l'hopital's rule it is equal to 1? Because when you differentiate the top and bottom you get cos theta/1 and substituting the limit you get cos(0)=1 and 1/1=1.

syndrac
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how about when there is a #x in the denominator rather than sin(#x) -- ex: sin(x)/5x

eXCey