## cluo Group Title limit of 17/14^x+25arctan(x^5) as x approaches infinity. one year ago one year ago

1. cluo Group Title

its the first one

2. cluo Group Title

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

3. cluo Group Title

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

4. cluo Group Title

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

5. walters Group Title

|dw:1360488025343:dw|

6. agent0smith Group Title

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

7. agent0smith Group Title

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

8. agent0smith Group Title

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

9. cluo Group Title

yes

10. agent0smith Group Title

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

11. walters Group Title

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

12. agent0smith Group Title

Hehe, still not the right function @walters

13. walters Group Title

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 Group Title

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

15. agent0smith Group Title

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

16. agent0smith Group Title

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 Group Title

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 Group Title

@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 Group Title

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

20. agent0smith Group Title

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

21. agent0smith Group Title

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 Group Title

kind of but not really

23. agent0smith Group Title

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

24. cluo Group Title

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

25. agent0smith Group Title

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 Group Title

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