Here's the question you clicked on:
cluo
limit of 17/14^x+25arctan(x^5) as x approaches infinity.
17/14^x is zero as x goes to infinity?
then 25arctan(x^5) is left right?
so can i get the solution without looking at the graph?
Yeah, arctan(x^5) will approach the same limit as arctan(x)
@walters i don't think that's the correct function
It is this, right??\[\frac{ 17 }{ 14^x}+25*\arctan(x^5)\]
lim x=> inf for arctan(x) is pi/2 if i recall correctly. Since we have 25arctan(x)... So 25pi/2.
ok it means it will be|dw:1360488400036:dw|
Hehe, still not the right function @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
how do you know the limit of arctan is pi/2?
@walters this is the function \[\frac{ 17 }{ 14^x}+25*\arctan(x^5) \]
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...
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?
@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
ok i see is my mistake |dw:1360488999424:dw| thx @agent0smith
there you go :) you had the limit correct in your earlier post, 25pi/2, just had the function written incorrectly.
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.
I'll get a graph... do you remember much on inverse functions?
if i look at a graph then i see it, nope everything is hazy. how do you retain that information after years?
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?
Plus it might be easier to remember that tan90 (degrees) is undefined.