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ggrree
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I have a question dealing with limits. (conceptual)
(see next post)
 2 years ago
 2 years ago
ggrree Group Title
I have a question dealing with limits. (conceptual) (see next post)
 2 years ago
 2 years ago

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ggrree Group TitleBest ResponseYou've already chosen the best response.1
say you had: \[\lim_{x \rightarrow 0} {\tan^8x \over x^8}\] would it be correct to say this?\[\lim_{x \rightarrow 0} ({\tan^x \over x})^8\] and then \[(\lim_{x \rightarrow 0} {\tan^x \over x}) ^8 = (1)^8\]
 2 years ago

ggrree Group TitleBest ResponseYou've already chosen the best response.1
I did the last step with lhospoitals' rule, by the way. done in one step.
 2 years ago

ggrree Group TitleBest ResponseYou've already chosen the best response.1
I'm wondering if it's ok to "bring the limit" inside the brackets, ignoring the ^8 exponential
 2 years ago

agreene Group TitleBest ResponseYou've already chosen the best response.0
your first step is a bit odd, and im not sure you can do exactly that...
 2 years ago

agreene Group TitleBest ResponseYou've already chosen the best response.0
after looking at this againi thought they were different exponents... \[\large \frac{\tan^8 x}{x^8}=(\frac{\tan x}{x})^8\] is true.
 2 years ago

ggrree Group TitleBest ResponseYou've already chosen the best response.1
yeah, I know the algebraic manipulations are OK, but is it ok to disregard the ^8 and bring the limit inside the brackets?
 2 years ago

bmp Group TitleBest ResponseYou've already chosen the best response.0
Seems okay to me. The resulting limit is the correct one, at least. This is interesting, though. Never thought about it :) Kudos, mate.
 2 years ago

bmp Group TitleBest ResponseYou've already chosen the best response.0
I wonder if that's the same as taking repetitive L'Hopital rules? I mean, since tanx/x will be 1 as x approaches 0
 2 years ago

gordonj005 Group TitleBest ResponseYou've already chosen the best response.2
i seem to remember this from calc: it's ok to bring the limit inside a function if the function is onetoone on the interval in question, this is to preserve inequalities in the epsilondelta definition of the limit
 2 years ago
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