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October 16th, 2009, 01:54 PM   #1
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trivial proof on limits?

Hi, I saw this question on a past test:

prove that x->3 1/(x-4) = -1

this looks very trivial, doesn't this just follow from the reciprocal limit law? take delta to be min(1/2, epsilon/2)
since all we have to do here is prove that you can plug "a" into the equation

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October 16th, 2009, 02:05 PM   #2
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Re: trivial proof on limits?

Basically, yeah.

We know that that function is continuous at 3 (prove it), so -1=f(3)= lim x->3 f(x)
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December 2nd, 2009, 07:42 PM   #3
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Re: trivial proof on limits?

quotient of continuous functions are continuous wherever the denominator is nonzero. The limit of a quotient is the quotient of the limits if the limit of the denominator is nonzero. The top is constant so the limit is the same, the bottom is linear and you can take lim(x-4) = lim(x) - lim(4) = lim(x) -4 = 3 -4 = -1. Done.
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