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!

How can I calculate left and right-sided limits?

  1. Aug 31, 2008 #1
    Hi,
    How can I calculate left and right-sided limits?
    [tex]\frac{x}{a}[\frac{b}{x}][/tex]
    [tex]\frac{b}{x}[\frac{x}{a}][/tex]
    [tex]\frac{x}{\sqrt{|sinx|}}[/tex]
    in point x=0.
    Thanks for help.
     
  2. jcsd
  3. Aug 31, 2008 #2

    statdad

    User Avatar
    Homework Helper

    Re: limits

    What have you done? think about how the definition of absolute value and how [tex] \sin x [/tex] behaves when [tex] x \approx 0 [/tex].
     
  4. Aug 31, 2008 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: limits

    For x not equal to 0, this is just b/a and so has b/a as both right and left sided limits.
    Or did you mean (x/a)|b/x|? In that case, you take left and right limits by looking at:
    If x> 0 then |b/x|= |b|/x so (x/a)(|b|/x)= |b|/a
    If x< 0 then |b/x|= -|b|/x so (x/a)(|b|/x)= -|b|/a

    Same comments

    The last one should be easy. Since sin(-x)= -sin(x), |sin(-x)|= |sin(x)| and the only difference between x< 0 and x> 0 is in the numerator.
     
  5. Aug 31, 2008 #4
    Re: limits

    [tex][\frac{b}{x}][/tex] it is entier function. I can not solve second case... It is harder than first. Can I do [tex](\frac{x}{a}-1)\frac{b}{x}\leq{[\frac{x}{a}]\frac{b}{x}}\leq{\frac{b}{a}}[/tex] and use [tex]|f(x)-g|\leq{\epsilon}[/tex] so [tex]g=\frac{b}{a}[/tex]?
     
  6. Aug 31, 2008 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: limits

    I don't know what that means.

    Where did the "-1" in [tex]\frac{x}{a}-1[/itex] come from?
     
  7. Aug 31, 2008 #6
    Re: limits

    [tex][\frac{b}{x}][/tex] the floor and ceiling functions.
    [tex]x-1\leq{[x]}\leq{x}[/tex]
     
  8. Sep 1, 2008 #7

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: limits

    Chose one! Does it mean the floor or the ceiling. It can't be both! If you mean [x] is the integer between x-1 and x, then it is the floor.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: How can I calculate left and right-sided limits?
  1. How can I linearize ? (Replies: 21)

Loading...