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Find the limit in question 7e and 7g?

  1. Dec 12, 2013 #1
    How can I find the limit in question 7e and 7g?
    Finding limits is difficult!:cry:
     

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  3. Dec 12, 2013 #2

    vanhees71

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    7e: I guess everything is within real calculus. Then you can argue that the sine is bound and thus the limit must be zero:
    [tex]0 \leq |x \sin(1/x)| \leq |x| \rightarrow 0.[/tex]

    7g: Expanding [itex]\sin(1/x)[/itex] around [itex]x \rightarrow \infty[/itex] gives
    [tex]x \sin(1/x)=x [1/x+\mathcal{O}(1/x^3)] \rightarrow 1.[/tex]
     
  4. Dec 12, 2013 #3
    How to derive this?
    Could you explain more,please?
     
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