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Mean Value Theorem Problem

  1. Oct 2, 2007 #1
    1. The problem statement, all variables and given/known data
    Show that sin x < x for all x > 0


    3. The attempt at a solution
    I thought I was pretty good at calculus so I have kinda been shifting my calc class onto the bottom of my todo list, but this mean value theorem problem is giving me some problems.

    For x > 1, sin x [tex]\leq[/tex] 1 < x

    This was my start.... after about 25 minutes of thinking about how the mean value theorem could be applied I looked in the back.. (with much reluctance, trust me). They chose 2pi instead of 1 for the first part, that is likely significant but I am not getting thepoint. They then proceed to prove that (sinx)/(x) = cos(c) for some c in (0,2pi) and I can see that at that point c sin x< x since cos(c)[tex]\leq 1[/tex] but ONLY at that point c... I don't see how it proves it for the general case in that interval...
     
    Last edited: Oct 2, 2007
  2. jcsd
  3. Oct 2, 2007 #2

    NateTG

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    Can you show that the slope of the tangent of [itex]\sin(x)[/itex] is less than one for [itex]0<x \leq 1[/itex]?

    Then, if you assume that there is a point with [itex]x>0,x=\sin(x)[/itex] what happens when you apply the mean value theorem?
     
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