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cluo
 2 years ago
limit of 17/14^x+25arctan(x^5) as x approaches infinity.
cluo
 2 years ago
limit of 17/14^x+25arctan(x^5) as x approaches infinity.

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cluo
 2 years ago
Best ResponseYou've already chosen the best response.017/14^x is zero as x goes to infinity?

cluo
 2 years ago
Best ResponseYou've already chosen the best response.0then 25arctan(x^5) is left right?

cluo
 2 years ago
Best ResponseYou've already chosen the best response.0so can i get the solution without looking at the graph?

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.2Yeah, arctan(x^5) will approach the same limit as arctan(x)

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.2@walters i don't think that's the correct function

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.2It is this, right??\[\frac{ 17 }{ 14^x}+25*\arctan(x^5)\]

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.2lim x=> inf for arctan(x) is pi/2 if i recall correctly. Since we have 25arctan(x)... So 25pi/2.

walters
 2 years ago
Best ResponseYou've already chosen the best response.1ok it means it will bedw:1360488400036:dw

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.2Hehe, still not the right function @walters

walters
 2 years ago
Best ResponseYou've already chosen the best response.1this means the answer is infinity sice the limit of the first part is infinity which will affect the second part of the function

cluo
 2 years ago
Best ResponseYou've already chosen the best response.0how do you know the limit of arctan is pi/2?

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.2@walters this is the function \[\frac{ 17 }{ 14^x}+25*\arctan(x^5) \]

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.2lim of arctanx is pi/2 because... tanx has asymptotes at pi/2, and arctanx is its inverse. There might be more proof needed than that though...

cluo
 2 years ago
Best ResponseYou've already chosen the best response.0i can see it is pi/2 on a graph when x goes to infinity but how to find it without a graph? or do you just memorize it?

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.2@cluo tan(x) is undefined for pi/2 radians. As x => pi/2, tanx approaches infinity. Therefore it's inverse, arctanx, is bounded between y= pi/2 and y= pi/2

walters
 2 years ago
Best ResponseYou've already chosen the best response.1ok i see is my mistake dw:1360488999424:dw thx @agent0smith

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.2there you go :) you had the limit correct in your earlier post, 25pi/2, just had the function written incorrectly.

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.2Make sense @cluo? The reason for the limit of arctanx as x => inf. is just due to arctanx being the inverse of tanx (tanx restricted to a domain pi/2 to pi/2)... since tanx is not onetoone, and thus doesn't have a valid inverse function w/o restriction.

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.2I'll get a graph... do you remember much on inverse functions?

cluo
 2 years ago
Best ResponseYou've already chosen the best response.0if i look at a graph then i see it, nope everything is hazy. how do you retain that information after years?

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.2haha, it took me a few mins to remember it, it wasn't instant. Maybe this will help: http://ocw.mit.edu/ans7870/18/18.013a/textbook/chapter01/images/tan_atan.gif See how the arctanx is *only* that part of tanx between x=pi/2 and pi/2?

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.2Plus it might be easier to remember that tan90 (degrees) is undefined.
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