I Trick for evaluating limits by substituting in 1/n

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Summary
Trick I vaguely remember from Calc 1
Hi, I remember some sort of method for evaluating limits from Calc 1 that involved substituting in 1/n for x and simplifying. Does that sound familiar to anyone? Sorry I know that's vague, but all I can really remember about it. I can't find it mentioned anywhere in Stewart nor online :/

Thank you...
 

RPinPA

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Well, that would change a ##\lim_{x \rightarrow \infty}## to a ##\lim_{n \rightarrow 0}## or ##\lim_{x \rightarrow 0}## to ##\lim_{n \rightarrow \infty}##. Perhaps there are cases where that's a useful thing to do, but it's not a trick I recall seeing off the top of my head.
 
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Summary: Trick I vaguely remember from Calc 1

Hi, I remember some sort of method for evaluating limits from Calc 1 that involved substituting in 1/n for x and simplifying. Does that sound familiar to anyone? Sorry I know that's vague, but all I can really remember about it. I can't find it mentioned anywhere in Stewart nor online :/

Thank you...
This substitution appears fairly often in calculus textbooks.
Given the limit ##\lim_{n \to \infty}(1 + \frac 1 n)^n##, you can use the substitution x = 1/n, and work with the new limit ##\lim_{x \to 0^+}(1 + x)^{1/x}## and evaluate the new limit.
 
I believe you are talking about the Heine Theorem.
 
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I believe you are talking about the Heine Theorem.
I don't think so.
I am not familiar with the Heine Theorem, but I did find online descriptions of the Heine-Borel Theorem and the Heine-Cantor Theorem, neither of which had anything to do with limits, as far as I could see.

Also, the OP mentioned that his question was about Calc 1, which focuses mostly on limits and differentiation.
 

WWGD

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I vaguely remember it used to compute derivatives somewhat similar to what Mark44 wrote , maybe in terms of dense subsets, as in :

##f'(x)=Lim_{ n \rightarrow \infty} [ f(x+1/n)-f(x)] / (1/n) ##

Let me try to remember more details.
 
For every function limit ## lim_{x -> x_0} f(x) = A ##, if there is a series s.t. ##lim_{n -> \infty} a_n = x_0##, then ## lim_{n -> \infty} f(a_n) = A##. By the way, ## lim_{x -> x_0} f(x) = A ## iff ##forall~a_n~s.t.~ lim_{n -> \infty} a_n = x_0, lim_{n -> \infty} f(a_n) = A##. This is what I mentioned.
 

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