Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

cluo

  • 2 years ago

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

  • This Question is Closed
  1. cluo
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its the first one

  2. cluo
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  3. cluo
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  4. cluo
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  5. walters
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1360488025343:dw|

  6. agent0smith
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  7. agent0smith
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  8. agent0smith
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  9. cluo
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  10. agent0smith
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  11. walters
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  12. agent0smith
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Hehe, still not the right function @walters

  13. walters
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  15. agent0smith
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  16. agent0smith
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @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
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  20. agent0smith
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  21. agent0smith
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    kind of but not really

  23. agent0smith
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  24. cluo
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  25. agent0smith
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  27. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.