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Real analysis

  1. Aug 1, 2010 #1
    [tex]{{\lim_{\substack{x\rightarrow\pi}} {\left( \frac {x}{x-\pi}{\int_{\pi}^{x} }\frac{sin t}{t}} dt\right)}[/tex]
  2. jcsd
  3. Aug 1, 2010 #2


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    First, of course, that "x" outside the integral goes to [itex]\pi[/itex]. The only problem is
    [tex]\lim_{x\to\pi}\frac{\int_\pi^x \frac{sin(t)}{t} dt}{x- \pi}[/tex]
    which gives the "0/0" indeterminate form.

    Use L'Hopital's rule to find that limit.
  4. Aug 1, 2010 #3


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    The expression is simply the derivative of the integral, i.e. the integrand at π, which is sin(π)/π = 0.
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