i know it is 1 but, i dont know how to get there..
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02-19-2009, 11:16 PM #1Junior Member
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Limit as x approaches infinity of xsin(1/x)?
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02-19-2009, 11:16 PM #2Junior Member
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lim x --> inf (xsin(1/x))
lim x --> inf (sin(1/x)/ 1/x)
lim x --> inf ((-1/x^2)cos(1/x)/ -1/x^2)
lim x ---> inf (cos(1/x))
cos(1/infinity) ~ cos(0) = 1
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02-19-2009, 11:16 PM #3Junior Member
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xsin(1/x) = sin(1/x)/(1/x)
by l'hopital's rule: lim = lim cos(1/x)ln(x)/lnx = lim cos(1/x) = 1, since cos(0) =1.
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