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

1. cluo

its the first one

2. cluo

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

3. cluo

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

4. cluo

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

5. walters

|dw:1360488025343:dw|

6. agent0smith

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

7. agent0smith

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

8. agent0smith

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

9. cluo

yes

10. agent0smith

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

11. walters

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

12. agent0smith

Hehe, still not the right function @walters

13. 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

14. cluo

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

15. agent0smith

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

16. 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...

17. cluo

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?

18. 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

19. walters

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

20. agent0smith

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

21. 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.

22. cluo

kind of but not really

23. agent0smith

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

24. cluo

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

25. 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?

26. agent0smith

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

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