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July 26th, 2010, 04:26 PM   #1
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Help plz with VERY beginner limits.

I suck at even the easiest of calculus that I'm trying to learn.
Like this easy question that I can't figure out.

limit (x-2) / (x^2-x-2)
x -> 2

I found the limit to be .33, but I don't think that's right.

********
Does limits always have to go to a whole number?

Thanks!
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July 26th, 2010, 04:31 PM   #2
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Re: Help plz with VERY beginner limits.

That's correct. The limit is 1/3.

Quote:
Do limits always have to go to a whole number?
No. Who told you that???
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July 26th, 2010, 04:33 PM   #3
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Re: Help plz with VERY beginner limits.

If by .33 you mean 1/3 then you are correct.



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July 26th, 2010, 05:08 PM   #4
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Re: Help plz with VERY beginner limits.

Thanks.
I think this makes sense now.

I have like 50 more practice questions so I'm sure I'm going to get confused again.

Thanks again for helping
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July 26th, 2010, 05:55 PM   #5
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Re: Help plz with VERY beginner limits.

Oh and I have another question.

Can all limits be put into a fraction such as 1/3, 1/4, 1/8, etc.
Are there such thing as a limit like: 0.2352354364564636346465745634523536577436345 where it can't be put into a fraction?
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July 26th, 2010, 06:09 PM   #6
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Re: Help plz with VERY beginner limits.

which is irrational, i.e. it can't be expressed as a fraction.

A limit may evaluate to any real number: a fraction, an integer, an irrational number and so on.
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August 1st, 2010, 02:13 PM   #7
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Re: Help plz with VERY beginner limits.

Factorizing made by greg1313, is the way which must always be checked first, but you can try L'Hospital's rule right from the beginning and this is very quick too: because if you calculate lim for x->2 you have form, you use L'Hospital's rule: (taking the first derivatives of both numerator and denominator).Hope this is helpful too.
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August 1st, 2010, 05:17 PM   #8
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Re: Help plz with VERY beginner limits.

Here's a quick "order of operations" (if you will, but I'm sure many won't!) for algebraic limits.
I assume you don't know about the hospital rule (yet)...
1. Direct substitution. If plugging in the value of x to which x approaches (call it "c") doesn't give you something crazy/undefined, then you're done.
2. Factor/polynomial long division. If you can cancel a factor of (x - c), you should be ready to use direct sub.
3. Conjugates. If you have a +/- sqrt(b) in the denominator, multiply the fraction by its conjugate (a -/+ sqrt(b)) and that should clear things up.

There are some tricks for evaluating trig limits, but we'll cross that bridge/bump that thread at a later date!
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