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onegirl Group Title

Find the function f(x) satisfying the given conditions. (HINT: You are finding the value of C)

  • one year ago
  • one year ago

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  1. onegirl Group Title
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    • one year ago
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  2. myininaya Group Title
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    Find \[\int\limits_{}^{}f'(x) dx=f(x)+C, \text{ where } (f)'=f'\]

    • one year ago
  3. myininaya Group Title
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    Or evaluate

    • one year ago
  4. myininaya Group Title
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    Integrate the function given to get from f' to f.

    • one year ago
  5. myininaya Group Title
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    Don't forget when you integrate, put +C.

    • one year ago
  6. onegirl Group Title
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    can u explain? :/

    • one year ago
  7. myininaya Group Title
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    \[\int\limits_{}^{}f'(x) dx=\int\limits_{}^{}(4x^2-1) dx\] You may find it easy to use the following: \[\int\limits_{}^{}x^n dx =\frac{x^{n+1}}{n+1}+C, n \neq -1\] This is because \[(\frac{x^{n+1}}{n+1})'=(n+1) \cdot \frac{x^{n+1-1}}{n+1}=x^{n+1-1}=x^n\] And you may also want to use \[\int\limits_{}^{}k dx=kx+C \text{ where} K, C \text{ are a constant} \]

    • one year ago
  8. myininaya Group Title
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    This is because (kx+C)'=(kx)'+(C)'=k(x)'+0+k(x)'=k(1)=k

    • one year ago
  9. onegirl Group Title
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    okay thanks

    • one year ago
  10. zepdrix Group Title
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    Are you familiar with the idea of `Integration` yet? Or has it only been introduced to you as the process of finding the `anti-derivative` so far?

    • one year ago
  11. onegirl Group Title
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    no i'm not familiar

    • one year ago
  12. onegirl Group Title
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    @Best_Mathematician can u help?

    • one year ago
  13. Loser66 Group Title
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    |dw:1367625325100:dw|

    • one year ago
  14. Loser66 Group Title
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    so, when you have f' (4x^2 +1) take integral to get back the original function. . when take integral, the solution for that method always a family solution. in case they give you the special solution, that means they want you to pick out just special C in set of family solution . take integral of f' you have f(x) = 4x^3/3 -x +C and when they give you f(0) =2 just plug 0 into the function you' ve just got. to find C f(0) = 4 *0^3/3 -0 +C = 2 ---> C =2 that's it

    • one year ago
  15. onegirl Group Title
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    ohhh okay

    • one year ago
  16. Loser66 Group Title
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    sorry , one more step. plug C back to f(x) = 4x^3/3 - x +2

    • one year ago
  17. Loser66 Group Title
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    I 'm supper dummy at teaching, hope you can understand what i mean

    • one year ago
  18. onegirl Group Title
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    so plugging 2 back into f(x) = 4x^3/3 - x + 2 right?

    • one year ago
  19. Loser66 Group Title
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    yep

    • one year ago
  20. onegirl Group Title
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    okay

    • one year ago
  21. onegirl Group Title
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    i got 32/3 or 10.6666

    • one year ago
  22. Loser66 Group Title
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    hey, you misunderstand the concept, they ask you to find out C, and you got C =2 that's it. just plug C =2 into the function, nothing to do more.

    • one year ago
  23. onegirl Group Title
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    ohh okay my bad

    • one year ago
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