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#1 2007-05-26 16:53:08
- Identity
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- Registered: 2007-04-18
- Posts: 934
Limit
How can I work out the limit of this??
Last edited by Identity (2007-05-26 17:15:04)
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#2 2007-05-26 17:04:38
- LQ
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- Registered: 2006-12-04
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Re: Limit
sin(that's alot)/inf = 0
Last edited by LQ (2007-05-26 17:23:28)
I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...
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#3 2007-05-26 17:15:19
- Identity
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- Registered: 2007-04-18
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Re: Limit
Sorry it was wrong, I edited it so it is correct now
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#4 2007-05-26 17:20:38
- LQ
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Re: Limit
Don't worry, the limit is still 0 since the function sin(5/x) circles between one and minus one.
so +/-0
I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...
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#5 2007-05-26 17:24:10
- Identity
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- Registered: 2007-04-18
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Re: Limit
Hmm, apparently when it is divided by 2x it takes on a different shape. It is like a truncus, and when my calculator takes the limit of the whole thing it gets
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#6 2007-05-26 18:00:38
- JaneFairfax
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- Registered: 2007-02-23
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Re: Limit
If you are using a calculator, you should make sure you are working in radians, not degrees!
Use the formula
Hence
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#7 2007-05-26 18:18:29
- LQ
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Re: Limit
okay, x on top now, didn't see that sorry.
I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...
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#8 2007-05-27 00:28:05
- mathsyperson
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- Registered: 2005-06-22
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Re: Limit
Ah, that's a very nice way of doing things. I'd have used L'Hopital myself, but that way is more elegant.
Why did the vector cross the road?
It wanted to be normal.
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#9 2007-05-27 01:49:38
- Identity
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- Registered: 2007-04-18
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Re: Limit
If you are using a calculator, you should make sure you are working in radians, not degrees!
Use the formula
Hence
Thanks Jane, where did u get the formula from?
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#10 2007-05-27 02:26:33
- mathsyperson
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- Registered: 2005-06-22
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Re: Limit
That's generally accepted as a standard formula. You could derive it by using the MacLaurin series of sin x.
sin x = x - x³/6 + x[sup]5[/sup]/120 - ...
As x gets close to 0, we can neglect the higher powers and so make the approximation that sin x = x.
From there, you can rearrange to get sinx/x = 1.
Why did the vector cross the road?
It wanted to be normal.
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