Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Lim (1/x)^tan(x) as x->0 ? help please..

  1. Nov 27, 2015 #1
    l'hopital must be apply, i'll be very grateful
     
  2. jcsd
  3. Nov 27, 2015 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hello felipe :welcome:

    Do you know the limit for ##\sin x \over x ## ?
     
  4. Nov 27, 2015 #3

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    oops, sorry, you mean $$x^{-\tan x}\ \ ?$$
     
  5. Nov 27, 2015 #4
    yes! the last
     
  6. Nov 27, 2015 #5

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Where does ##\ x^{\tan x}\ ## go for ## \ x\downarrow 0 ## ?
     
  7. Nov 27, 2015 #6
    lim ( 1/x )^tan x as x->0
     
  8. Nov 27, 2015 #7

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, that was my question :smile:
     
  9. Nov 27, 2015 #8
    I dont understand your question :frown: (my english is not very good)
     
  10. Nov 27, 2015 #9

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    What is the limit ##\ \ \displaystyle \lim_{x\downarrow 0}
    \ x^{\tan x}\ ## ?
     
  11. Nov 27, 2015 #10

    mathman

    User Avatar
    Science Advisor
    Gold Member

    tanx ~ x as x ->0, so problem can be looked at as [itex]\lim_{x-->0} x^x[/itex] However [itex]x^x=e^{xlnx}[/itex].
    Since [itex]\lim_{x->0}xlnx=0[/itex], the final answer = 1.
     
  12. Nov 27, 2015 #11
    thanks
     
  13. Nov 28, 2015 #12
    Tan (0)=0 there for answer will be 1
     
  14. Nov 28, 2015 #13

    mathman

    User Avatar
    Science Advisor
    Gold Member

    Not by itself. The function is [itex](\frac{1}{x})^{tanx}[/itex], so as x->0, the expression becomes [itex](\frac{1}{0})^{0}[/itex] which is indeterminate.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Lim (1/x)^tan(x) as x->0 ? help please..
  1. Lim x to 0 x*sin(1/x) (Replies: 12)

Loading...