anonymous
  • anonymous
limit of 17/14^x+25arctan(x^5) as x approaches infinity.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
its the first one
anonymous
  • anonymous
17/14^x is zero as x goes to infinity?
anonymous
  • anonymous
then 25arctan(x^5) is left right?

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anonymous
  • anonymous
so can i get the solution without looking at the graph?
walters
  • walters
|dw:1360488025343:dw|
agent0smith
  • agent0smith
Yeah, arctan(x^5) will approach the same limit as arctan(x)
agent0smith
  • agent0smith
@walters i don't think that's the correct function
agent0smith
  • agent0smith
It is this, right??\[\frac{ 17 }{ 14^x}+25*\arctan(x^5)\]
anonymous
  • anonymous
yes
agent0smith
  • agent0smith
lim x=> inf for arctan(x) is pi/2 if i recall correctly. Since we have 25arctan(x)... So 25pi/2.
walters
  • walters
ok it means it will be|dw:1360488400036:dw|
agent0smith
  • agent0smith
Hehe, still not the right function @walters
walters
  • walters
this means the answer is infinity sice the limit of the first part is infinity which will affect the second part of the function
anonymous
  • anonymous
how do you know the limit of arctan is pi/2?
agent0smith
  • agent0smith
@walters this is the function \[\frac{ 17 }{ 14^x}+25*\arctan(x^5) \]
agent0smith
  • agent0smith
lim 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...
anonymous
  • anonymous
i 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
  • agent0smith
@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
  • walters
ok i see is my mistake |dw:1360488999424:dw| thx @agent0smith
agent0smith
  • agent0smith
there you go :) you had the limit correct in your earlier post, 25pi/2, just had the function written incorrectly.
agent0smith
  • agent0smith
Make 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 one-to-one, and thus doesn't have a valid inverse function w/o restriction.
anonymous
  • anonymous
kind of but not really
agent0smith
  • agent0smith
I'll get a graph... do you remember much on inverse functions?
anonymous
  • anonymous
if i look at a graph then i see it, nope everything is hazy. how do you retain that information after years?
agent0smith
  • agent0smith
haha, 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
  • agent0smith
Plus it might be easier to remember that tan90 (degrees) is undefined.

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