1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

PUHLEAZE help with this limit

  1. Oct 13, 2006 #1
    okay, here I have a problem with this limit, i used every method i know of and could solve it... any help or something to get started with be appreciated

    [tex] \lim_{\x\rightarrow 1^{-}\} \frac{\sqrt[3]{\arctan(x)} - \arccos(\sqrt[3]{x}) - \sqrt[3]{frac{\pi}{4}}{x-1}[/tex]

    okay i tried ti put x=cos^3 (X) but couldnt get to a result
    I tried to use the x^3 - y^3 = (x-y)(x²+xy+y²) but no result
    i tried everything :-S

    PS: we didnt learn the derivative function of arctanx ...
  2. jcsd
  3. Oct 13, 2006 #2
    i think the latex hasnt worked... it was :
    the limit when x tends to 1- of :
    [arctan(x)]^(1/3) - arccos [x^(1/3)] - (pi/4)^(1/3)

    [tex] \lim_{\x\rightarrow 1^{-}\} \frac{\sqrt[3]{\arctan(x)}-\arccos(\sqrt[3]{x}) - \sqrt[3]{frac{\pi}{4}}{x-1}[/tex]
    Last edited: Oct 13, 2006
  4. Oct 13, 2006 #3
    Use L'Hopitals rule. [tex] \frac{d}{dx} \arctan x = \frac{1}{1+x^{2}} [/tex]
  5. Oct 13, 2006 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    He isn't allowed to know the derivative of arctan..:frown:
  6. Oct 13, 2006 #5
    yeah right... :-s
  7. Oct 13, 2006 #6
    [tex]\lim_{y\rightarrow 0}\frac{sin(y)}{y}[/tex]
  8. Oct 13, 2006 #7
    umm equals one ?! so ...
  9. Oct 14, 2006 #8
    still no one !? :confused:
  10. Oct 14, 2006 #9
    here is it...
    [tex]\lim_{x \rightarrow 1^{-}} \frac{\sqrt[3]{\arctan x} - \arccos \sqrt[3]{x} - \sqrt[3]{\frac{\pi}{4}}}{x-1}[/tex]
  11. Oct 14, 2006 #10
    woops, yea sorry was trying to get your limit to show up... Something weird musta happened. Sorry.
  12. Oct 14, 2006 #11
    I realize that this is the derivative of [tex] \sqrt[3]{\arctan x} - \arccos \sqrt[3]{x} [/tex] at the point 1. But I guess that doesnt help since I am not supposed to use the derivatives
  13. Oct 14, 2006 #12
    why not look at the graph?
  14. Oct 14, 2006 #13
    okay... here is what i have done so far........
    let's put [tex]\cos^{3}y = x[/tex]
    so the function becomes:
    [tex]\lim_{y \rightarrow 1^{-}} \frac{\sqrt[3]{\arctan \cos^{3}y} - \arccos \sqrt[3]{\cos^{3}y} - \sqrt[3]{\frac{\pi}{4}}}{(\cos^{3}y-1)}[/tex]
    which is equal to
    [tex]\lim_{y \rightarrow 1^{-}} \frac{\arctan \cos^{3}y - \frac{\pi}{4}} {(\cos^{3}y-1)(\sqrt[3]{\arctan \cos^{3}y}^{2} + \sqrt[3]{\frac{\pi}{4}}^{2} + \sqrt[3]{\arctan \cos^{3}y} \sqrt[3]{\frac{\pi}{4}})} - \frac{y}{\cos^{3}y-1}[/tex]
    which is +infinity

    okay but there is one thing wrong here... [tex]\arccos \sqrt[3]{\cos^{3}y}[/tex] is not equal to y because [tex]\sqrt[3]{\cos^{3}y}[/tex] should be in the interval (0,pi), but actually, it's on the interval of (-pi/2 , pi/2) |because when cos^3y is positive only between -pi/2 and pi/2.
    know what I'm sayin :confused:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: PUHLEAZE help with this limit
  1. Help with Limits (Replies: 5)

  2. Help with limits (Replies: 4)

  3. Help with a limit (Replies: 3)

  4. Help with a limit. (Replies: 1)

  5. Limit help (Replies: 3)