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Math Help - Real Analysis Problem

  1. #1
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    Question Real Analysis Problem

    Let f: (0,1] -> R be differentiable on (0,1], with |f(x)|<=1 for all x in (0,1]. For each n in N, let a(sub n)=f(1/n). Show that a(sub n), with n in N, converges.
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  2. #2
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    Quote Originally Posted by dhhnerd View Post
    Let f: (0,1] -> R be differentiable on (0,1], with |f(x)|<=1 for all x in (0,1]. For each n in N, let a(sub n)=f(1/n). Show that a(sub n), with n in N, converges.
    Let f(x) = \sin \tfrac{1}{x} then f is differenciable on (0,\infty) and |f|\leq 1. The sequence is a_n = f(\tfrac{1}{n}) = \sin (n).
    However, \{a_n\} is not a convergent sequence.
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