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!

Find the value of this limit

  1. Dec 24, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the value of the limit of the following two questions when x is tending to zero.


    2. Relevant equations


    [ (tan x)/(x) ]
    [ (sin x ) / ( x ) ]

    Where [ ] is the gint function..


    3. The attempt at a solution

    If the question was w/o gint then both these limits were 1 (right?)

    But for gint have to check the graph of

    y=x , y=sinx ,y=tanx,

    so graph of tanx is above x which is above sinx ( x just after 0 )


    So 1st q answer=1

    2nd q answer=0

    Why is this wrong?
     
  2. jcsd
  3. Dec 24, 2013 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    I agree with your answers. What are the given answers?
     
  4. Dec 24, 2013 #3
    unfortunately i dont have the answers with me atm but ill post as soon as i get my hands on them.

    here's another question similar to this{pointless to make a new post out of it}


    [x^2/sinxtanx] where again [] is the gint function.


    so i look at it like two functions.


    (x/sinx)(x/tanx) one is tending to just below 0 while the other just greater than 1 but what will happen with the gint :x

    Help!
     
  5. Dec 24, 2013 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You mean, one is tending to just below 1 while the other just greater than 1, right?
    Yes, separating them like that is not going to help.
    It might help to boil the trig functions down to one trig function. I tried replacing the tan with sin/cos, but that didn't help. Do you know the "tan-half-angle" formulae, i.e. how sin(x), cos(x), tan(x) can be written in terms of t = tan(x/2)?
     
  6. Dec 25, 2013 #5
    You mean sin2x= 2tanx/1+tan^2(x)?


    Dont really think this is helping :X
     
  7. Dec 25, 2013 #6

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    It works for me. Please post what you get. (I wrote u = x/2, t = tan(u), and converted all to an expression using t and u.)
     
  8. Dec 28, 2013 #7
    okay you're right it worked for this question and certain similar question related to gint and sinx in it

    Thanks!


    Will keep this in mind :D
     
  9. Dec 29, 2013 #8

    vanhees71

    User Avatar
    Science Advisor
    2016 Award

    These are typical examples for the use of de L'Hospital's rule or (equivalently) doing a series expansion of numerator and denominator around the limit of [itex]x[/itex] (i.e., here around [itex]x=0[/itex]).
     
  10. Dec 30, 2013 #9
    how does one apply L'h rule when the functions like gint/ fraction etc are involved?
     
  11. Dec 30, 2013 #10

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    If the functions are not differentiable, that is not possible in a direct way. It can still help in some way (that depends on the function), but you still have to consider the gint brackets.
     
  12. Dec 31, 2013 #11

    vanhees71

    User Avatar
    Science Advisor
    2016 Award

  13. Dec 31, 2013 #12

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I assume it's ceiling. You can also attack problems like this by looking at the taylor series of the differentiable part around x=0.
     
    Last edited: Dec 31, 2013
  14. Dec 31, 2013 #13
    gint(x)= greatest integer equal to or less than x.
    I'm sorry for not naming it aptly ( this is what the folks call it down here)
     
  15. Dec 31, 2013 #14
    Hmm "dick" i hear what you're saying.

    Thank you.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Find the value of this limit
Loading...