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math456 Group Title

Help.. Prove that lim as x approaches to 0. x^4cos(2/x)=0

  • one year ago
  • one year ago

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  1. math456 Group Title
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    |dw:1347737098765:dw|

    • one year ago
  2. Mikael Group Title
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    Look ziz iz a seempl applicashion of limit lohz:|dw:1347737182410:dw|

    • one year ago
  3. Mikael Group Title
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    Now , since \[\lim_{x \rightarrow 0} \cos(x) = 1\]

    • one year ago
  4. math456 Group Title
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    yea

    • one year ago
  5. Mikael Group Title
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    And, on the other hand \[\lim_{x \rightarrow 0} x^4 = 0\]

    • one year ago
  6. Mikael Group Title
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    You have the product of those two being (surprise , surprise !) 0

    • one year ago
  7. math456 Group Title
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    gotch yaa..!!!

    • one year ago
  8. math456 Group Title
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    thank you!!

    • one year ago
  9. Mikael Group Title
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    Ahh sorry it is 2/x so here is the correct solution:

    • one year ago
  10. Mikael Group Title
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    Theorem we all can use states that Product of a Bounded function by another function that tends to zero - also tends to ZERO in the same limit

    • one year ago
  11. RaphaelFilgueiras Group Title
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    use squeeze theorem

    • one year ago
  12. Mikael Group Title
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    Buut\[|\cos(\frac{2}{x})| \leq 1, alwayz\]

    • one year ago
  13. Mikael Group Title
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    So we do have true the required assumptions: One of the factors (i.e. cos 2/x) is a bounded function while the other factor : x^4 tends to 0 when x-->0

    • one year ago
  14. RaphaelFilgueiras Group Title
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    |dw:1347737519682:dw|

    • one year ago
  15. math456 Group Title
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    yea i got it

    • one year ago
  16. Mikael Group Title
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    Medal ?

    • one year ago
  17. math456 Group Title
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    thank you both!!

    • one year ago
  18. Mikael Group Title
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    Thanks @math456

    • one year ago
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