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eiya

  • 2 years ago

evaluate lim (x-->0) S(x)/(X^3) if S(x)= int (from 0 to x) sin (0.5*pi*t^2)

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  1. Koikkara
    • 2 years ago
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    well, it will be helpful, if u could tell us which grade r u in..?

  2. eiya
    • 2 years ago
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    univrsity..

  3. Koikkara
    • 2 years ago
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    Fourier series?

  4. eiya
    • 2 years ago
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    no...only applying indeterminate forms and L'hospital's Rule chapter

  5. Koikkara
    • 2 years ago
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    well, may take some time...|dw:1363454097397:dw|

  6. eiya
    • 2 years ago
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    i can see yr hardness to write it....appreciate a lot..!

  7. Koikkara
    • 2 years ago
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    @Preetha ....posiibility is like she <<can help you.....

  8. Preetha
    • 2 years ago
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    Nah. I dont have a clue! Try @klimenkov

  9. AravindG
    • 2 years ago
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    how is t related to x ?

  10. eiya
    • 2 years ago
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    actually there "dt" after the close bracket

  11. AravindG
    • 2 years ago
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    thats better :)

  12. klimenkov
    • 2 years ago
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    \[\lim\limits _{x\rightarrow0}\frac{\int\limits _0^x\sin\frac{\pi t^2}2 dt}{x^3}\] When \(x\rightarrow0\), \(\int\limits _0^x\sin\frac{\pi t^2}2 dt\sim\frac{\pi x^3}{6}\), because \(\sin\frac{\pi t^2}2\sim\frac{\pi t^2}{2}\), when \(t\rightarrow0\). So the limit is \(\frac{\pi}{6}\).

  13. eiya
    • 2 years ago
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    are you applying fundamental theorem?

  14. klimenkov
    • 2 years ago
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    Lol. I have just read what you wrote above about L'hopital's rule. \(\left(\int\limits _0^x\sin\frac{\pi t^2}2 dt\right)'_x=\sin\frac{\pi x^2}2\) \(\left(\sin\frac{\pi x^2}2\right)'_x=\pi x\cos\frac{\pi x^2}2\) So we have \(\lim\limits _{x\rightarrow0}\frac{\int\limits _0^x\sin\frac{\pi t^2}2 dt}{x^3}=\lim\limits _{x\rightarrow0}\frac{\sin\frac{\pi x^2}2}{3x^2}=\lim\limits _{x\rightarrow0}\frac{\pi x\cos\frac{\pi x^2}2}{6x}=\lim\limits _{x\rightarrow0}\frac{\pi \cos\frac{\pi x^2}2}{6}=\frac \pi 6\), because \(\lim\limits_{x\rightarrow0}\cos\frac{\pi x^2}2=1\).

  15. eiya
    • 2 years ago
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    thanks a lot....but im trying to understand the steps..

  16. klimenkov
    • 2 years ago
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    Do you know the L'hopital's rule?

  17. eiya
    • 2 years ago
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    a bit...just learnt last month

  18. klimenkov
    • 2 years ago
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    Do you know what is the derivative?

  19. eiya
    • 2 years ago
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    nahh...i got it...understand already....

  20. eiya
    • 2 years ago
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    yes...i know derivative...

  21. eiya
    • 2 years ago
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    thank you..!

  22. klimenkov
    • 2 years ago
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    You are welcome.

  23. mathslover
    • 2 years ago
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    Welcome to OpenStudy @eiya

  24. mathslover
    • 2 years ago
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    http://prezi.com/fs3hqdpcopic/an-unofficial-guide-to-openstudy/ ^ A guide for you to start your journey well in openstudy @eiya

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