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Originally Posted by daking
y=sin(x)/x
at x = 0, we have y=0/0 which is undefined. But ofcourse by the limit as x tends to zero is 1 by l'hopitals rule
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Quote:
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Originally Posted by filtherton
The limit is zero.
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daking is correct the limit is 1.
The limit of y=sin(x)/x = 0/0, using l'hopital's rule the limit of y=cos(x)/1 as x->0 = cos(0)/1 = 1/1
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Originally Posted by daking
If we permit this kind of notation to enter mathematical proof sin(x)/x as x tends to infinity would be represneted as sin(infinity)/infinity. Then one might theorize that sin(infinity) is always less than 1 and so a finite number leading to the conclusion that the limit is 0. Where as the limit is obviously 1.
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Wow, how is the limit of sin(x)/x as x->inf obviously 1?
This limit is obviously 0, since |sin(x)|<=1. Limit of |sin(x)|/x as x->inf = 0. Take a look at the epsilon delta definition of limit why this works.