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knowLittle
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Homework Statement
Prove that
## lim_{x\implies 1} \frac{2}{x-3} = -1 ##
Use delta-epsilon.
The Attempt at a Solution
Proof strategy:
## | { \frac{ 2}{x-3} +1 } | < \epsilon #### \frac{x-1}{x-3} < \epsilon ##
, since delta have to be a function of epsilon alone and not include x. I need to restrict delta
## |x-1 | < 1 \leq \delta \\ -3 < x-3 < -1 ##
I know that there's something wrong. Help?
What if I say that
## -2 = x -3 \\ 1 =x \\ \frac{ 1-1}{-2} < \epsilon \\ \delta=min(1, \epsilon)##
Does it make any sense?
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