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kabulis

  • 2 years ago

determine if existent the limit: lim -->0 sinx-x/x^3

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  1. etemplin
    • 2 years ago
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    can you put parenthesis to make the problem a little more clear?

  2. Eda2012
    • 2 years ago
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    is it \[\lim_{x \rightarrow 0} \frac{ sinx-x }{ x^{3} }\]

  3. kabulis
    • 2 years ago
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    Yes that is the exact question.. @Eda2012

  4. Dido525
    • 2 years ago
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    Can you use :'hopital's rule?

  5. Dido525
    • 2 years ago
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    L'hopital's rule*

  6. kabulis
    • 2 years ago
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    Yes, we can use Hopital rule!

  7. etemplin
    • 2 years ago
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    that makes it so much easier @Dido525 thanks for thinking of that

  8. Dido525
    • 2 years ago
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    Okay then! Take the derivative of the top and bottom terms :) . But before that check if the limit is 0/0 or infinity/ infinity.

  9. Dido525
    • 2 years ago
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    Haha. I always ask ^_^ .

  10. Dido525
    • 2 years ago
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    Yeah the limit is 0/0 if you directly sub in.

  11. kabulis
    • 2 years ago
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    I need to show step by step to the professor :( lol... can anybody do that for me.. sorry guys

  12. Dido525
    • 2 years ago
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    |dw:1352266897769:dw|

  13. kabulis
    • 2 years ago
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    Thanks @Dido525

  14. Dido525
    • 2 years ago
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    Welcome!

  15. Eda2012
    • 2 years ago
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    \[1^{st} \] \[\frac{ dy }{ dx }= \lim_{x \rightarrow 0}\frac{ cosx-1 }{ 3x ^{2} }\] \[2^{nd}\] \[\frac{ dy }{ dx } = \lim_{x \rightarrow 0}\frac{ -sinx }{ 6x }\] \[3^{rd}\] \[\frac{ dy }{ dx }=\lim_{x \rightarrow 0}\frac{ -cosx }{ 6 }\] \[=-\frac{ 1 }{ 6 }\]

  16. Dido525
    • 2 years ago
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    Yeah. You often have to use L'hopital's rule multiple times.

  17. kabulis
    • 2 years ago
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    thnx all... what will be the solution if we use the rule L'hopital? since that is the required

  18. Eda2012
    • 2 years ago
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    the L'hopital's rule ...u must not get \[\frac{ \infty }{ \infty } or \frac{ 0 }{ 0 }\] when u plug in the lim of x....because the equation will become undefined for every value of x...that's why u have to use the rule many times until u get the actual value that can be defined....

  19. mahmit2012
    • 2 years ago
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    |dw:1352268277086:dw|

  20. mahmit2012
    • 2 years ago
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    |dw:1352268373043:dw|

  21. Eda2012
    • 2 years ago
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    @mahmit2012 ...r u using the divergent test...???

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