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Math Help - Double-check this limit please

  1. #1
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    Double-check this limit please

    Can someone double-check my work here? Thanks, if you can.

    <br />
\lim_{x\to\infty}[x(1-cos(1/x))]<br />

    Put x to the denominator to use L'Hopital's rule, etc. Applied chain rules, etc.

    <br />
\lim_{x\to\infty}[sin(1/x)]<br />

    Thus, if x goes to infinity, the above is sin(0) = 0. Final Answer: Zero
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  2. #2
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    Yes, it's okay, but you don't need that rule, you can turn that limit into a known one with a simple substitution.
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  3. #3
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    Oh, really? What is this substitution?
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  4. #4
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    t=\frac1x.
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  5. #5
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    tx=1

    so itequals to lim [(1-cost)/t]
    t->0
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