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anonymous

  • one year ago

My Achilles heel...

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  1. anonymous
    • one year ago
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    |dw:1439212533266:dw|

  2. phi
    • one year ago
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    you could write 3 as \( e^{\ln3 } \)

  3. anonymous
    • one year ago
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    I cant find that in my equation page..

  4. anonymous
    • one year ago
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    what happends to x?

  5. anonymous
    • one year ago
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    So how would u go on from there?

  6. phi
    • one year ago
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    use \[ \left(a^b\right)^c = a^{bc} \]

  7. phi
    • one year ago
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    \[ \int 3^x \ dx = \int \left(e^{\ln3}\right)^x \ dx\\ = \int e^{\ln 3 \ x} \ dx \]

  8. phi
    • one year ago
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    which is in the form \[ \int e^{ax} \ dx \]

  9. anonymous
    • one year ago
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    ok please continue, Ive had problem with these types, but ur explanation makes it easier.

  10. phi
    • one year ago
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    can you integrate \[ \int e^{ax} \ dx \] ? this is a "standard" integral

  11. anonymous
    • one year ago
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    Ive forgotten

  12. phi
    • one year ago
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    what is the derivative of e^x ?

  13. anonymous
    • one year ago
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    I have a problem with math, if I dont keep doing it, I fforget it..

  14. phi
    • one year ago
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    this one is worth looking up

  15. anonymous
    • one year ago
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    okey, I will go through that chapter again...can u guide me through this one?

  16. phi
    • one year ago
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    \[ \frac{d}{dx} e^{a x}= e^{ax} \frac{d}{dx} ax = a\ e^{ax}\]

  17. phi
    • one year ago
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    your problem is to "undo that" in other words \[ \int e^u \ du \] where u = ax \[ du = a \ dx\]

  18. phi
    • one year ago
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    and \[ \int e^u \ du = e^u \]

  19. anonymous
    • one year ago
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    ok, I will have to go through this chapter again, I seem to be forgetting..also Im tired, thank you !:)

  20. Loser66
    • one year ago
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    Trick: to find \(\int 3^x dx\), we need find "something" whose derivative = \(3^x\), right? let see, \((3^x)'= 3^x ln 3\) not \(3^x\), but ln3 is a constant, so, we just divide the original one by ln3. I meant \((\dfrac{3^x}{ln3})' = (\dfrac{1}{ln3} *3^x)'= \dfrac{1}{\cancel{ln3}}3^x *\cancel{ln3}=3^x\) hence \(\int 3^x dx = \dfrac{3^x}{ln3}+C\)

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is replying to Can someone tell me what button the professor is hitting...

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