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What is the limit of cos of x as x approaches infinity?
Old 09-27-2008, 04:38 PM   #1 (permalink)
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What is the limit of cos of x as x approaches infinity?

I understand that it osculates between 1 and -1, so is there a limit? Thanks for your help!
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Old 09-27-2008, 04:40 PM   #2 (permalink)
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There is no limit. As you have said the cosine function continually moves between -1 and 1. This means that it does not get continually closer to some fixed value which is the definition of a limit.
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Old 09-27-2008, 04:40 PM   #3 (permalink)
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There is no limit. As you have said the cosine function continually moves between -1 and 1. This means that it does not get continually closer to some fixed value which is the definition of a limit.
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Old 09-27-2008, 04:40 PM   #4 (permalink)
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There is no limit. As you have said the cosine function continually moves between -1 and 1. This means that it does not get continually closer to some fixed value which is the definition of a limit.
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The sense of limits approaching infinity in periodic functions
Old 09-15-2009, 08:26 AM   #5 (permalink)
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At The sense of limits approaching infinity in periodic functions

Very good question. I also asked myself how much is
lim (cos x) .
x-->∞
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Old 09-27-2009, 09:58 PM   #6 (permalink)
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thanks
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Old 10-05-2010, 05:20 AM   #7 (permalink)
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Lim (cos(1/x))^(x^2) as x--> infinity
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Old 07-08-2011, 01:47 PM   #8 (permalink)
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I WOULD SAY THE ANSWER IS NO LIMIT, OR D.N.E. DOES NOT EXIST
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Old 10-26-2011, 12:01 AM   #9 (permalink)
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i need help with a question:
the minute hand on a watch is 8mm long and the hour hand is 4mm long. how fast it the distance between the tips of the hands changing at 1 oclock? Thanks !
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Old 03-05-2013, 01:31 AM   #10 (permalink)
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"Lim (cos(1/x))^(x^2) as x--> infinity"

Well, first look at what's put inside the cosine function. As x approaches infinity when you have 1/x, that's 1 being divided by VERY large numbers which we can thus conclude is equivalent to 0. Taking the cos(0) you'll get 1.

So now we have 1^(x^2) as x approaches infinity, but the (x^2) is now kinda useless at this point; 1 raised to any power is 1.

Thus, the limit is 1.
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