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3 variable limit problem.sighs

  1. Nov 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Determine whether the following limit exist. If so, find its value

    [sin (x^2 + y^2 + z^2 )] / [(x^2 + y^2 + z^2)^1/2)]
    as x,y,z approach 0,0,0


    3. The attempt at a solution

    i tried to do using the limit of sin Ѳ / Ѳ as Ѳ approaching 0

    im from malaysia and this is my assignment question and i cant figure out the way to solve this question
     
  2. jcsd
  3. Nov 25, 2009 #2
    I'm not sure if this is right, but here's my attempt:
    Let u = x^2 + y^2 + z^2
    limit of u approaching 0 of [sin u] / [u^.5]
    sin(0) / [0^.5] = 0/0

    Therefore, you can use L'hopital's rule.
    sin u / u^.5
    cos u / .5u^(-.5)
    2cos u / (1/u^.5)
    2cos u (u^.5)
    u = x^2 + y^2 + x^2 = 0 so 2cos(0)(0) = 0.
     
  4. Nov 25, 2009 #3
    hey thanks for ur reply!
    im not sure if its correct cos i dont know either! =)
    but, a million thanks to u for replying!

    anyone have some more opinions?
    i wud love to discuss more about this =)
     
  5. Nov 25, 2009 #4

    HallsofIvy

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    Science Advisor

    As you say, with [itex]u= x^2+ y^2+ z^2[/itex],
    [tex]\frac{sin(x^2+y^2+ z^2)}{(x^2+ y^2+ z^2)^{1/2}}= \frac{sin(u^2)}{u}[/tex]
    Multiply both numerator and denominator by u to write that as
    [tex]u\frac{sin(u^2)}{u^2}[/tex]
    and now use [itex]sin(\theta)/\theta[/itex].
     
  6. Nov 25, 2009 #5
    thanks a lot dat really makes my day both of u gave me the same way of solutions and i think it is the best solution
    thanks!
     
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