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Homework Help: Draw a graph of xcos(1/x)

  1. May 8, 2014 #1
    1. The problem statement, all variables and given/known data
    Draw a graph of xcos(1/x)

    2. The attempt at a solution

    I've differentiated the equation using the product rule.

    This got me to:

    cos(1/x) + sin(1/x)/x

    What I don't know how to do is actually go about drawing the graph. This is also a past paper question for an exam where I won't be allowed calculators.

  2. jcsd
  3. May 8, 2014 #2


    User Avatar
    Homework Helper

    Calculators won't help you with that.

    (1) [itex]-x \leq x\cos(1/x) \leq x[/itex].
    (2) [itex]\cos(1/x) \to 1[/itex] as [itex]x \to \infty[/itex].
    (3) How fast does [itex]\cos(1/x)[/itex] oscillate at [itex]x \to 0[/itex]?
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