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Limits problemneed some help

  1. Sep 9, 2008 #1
    Show x<(or equal) xsin(1/x) <(or equal) -x if x<0

    and -|x| <(or equal) xsin(1/x) <(or equal) |x| if x cant be 0
     
  2. jcsd
  3. Sep 9, 2008 #2
    Well, we know that sine and cosine are bounded right?

    so [tex] |sin(a)|\leq 1[/tex] wich means that

    [tex] -1\leq sina \leq 1[/tex] now in your first part replace a by 1/x than multiply both sides by x, since x is smaller than zero, your inequality sides switch. procede similarly in 2.
     
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