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

- anonymous

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

- schrodinger

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- anonymous

its the first one

- anonymous

17/14^x is zero as x goes to infinity?

- anonymous

then 25arctan(x^5) is left right?

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## More answers

- anonymous

so can i get the solution without looking at the graph?

- walters

|dw:1360488025343:dw|

- agent0smith

Yeah, arctan(x^5) will approach the same limit as arctan(x)

- agent0smith

@walters i don't think that's the correct function

- agent0smith

It is this, right??\[\frac{ 17 }{ 14^x}+25*\arctan(x^5)\]

- anonymous

yes

- agent0smith

lim x=> inf for arctan(x) is pi/2 if i recall correctly. Since we have 25arctan(x)... So 25pi/2.

- walters

ok it means it will be|dw:1360488400036:dw|

- agent0smith

Hehe, still not the right function @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

how do you know the limit of arctan is pi/2?

- agent0smith

@walters this is the function \[\frac{ 17 }{ 14^x}+25*\arctan(x^5) \]

- 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

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

@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

ok i see is my mistake
|dw:1360488999424:dw|
thx @agent0smith

- agent0smith

there you go :) you had the limit correct in your earlier post, 25pi/2, just had the function written incorrectly.

- 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

kind of but not really

- agent0smith

I'll get a graph... do you remember much on inverse functions?

- anonymous

if i look at a graph then i see it, nope everything is hazy. how do you retain that information after years?

- 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

Plus it might be easier to remember that tan90 (degrees) is undefined.

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