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March 24, 2017

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What is the lim of the square root of x times sin of (1/x) as x approaches infinity

  • Calc 2 - ,

    x^.5 * sin (1/x)
    as 1/x ---> 0 , sin (1/x) = 1/x

    x^.5 * x^-1 = x^-.5 = 1/sqrt x
    which = 0 as x ---> infinity

  • Calc 2 - ,

    or, by this time you have probably seen L'Hospital's Rule, so

    limit √x sin(1/x)
    if u = 1/x, then we have
    limit sin(u)/√u
    = limit cos(u)/(1/2√u)
    = limit 2√u cos(u) as u->0
    = 0

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