I just want to know, in calculating limits, when I do direct substitution, and it gives 3/0 instead of 0/0, does it mean for sure that the limit does not exist?
Finding if the limit does not exist
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calculus
limits
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0@Hurkyl: Agreed. What I usually try to do is to gauge the academic level the questioner is at, and try to answer in $a$precise way roughly at that level, perhaps pushing *a little* beyond. – 2012-09-16
1 Answers
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Yes, it does mean that. Suppose $b_n\to 0$ and $c_n:=\frac{a_n}{b_n}\to L\in \mathbb R$. Then $\lim_{n\to\infty} a_n = \lim_{n\to\infty}b_n c_n=0\cdot L=0.$
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0@CameronBuie: Yes. Hagen is on the right way (+1). Thanks for lighting my mind. – 2012-09-15