Dido525
Find f(4) if f(x) is defined by:
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Dido525
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|dw:1353113377129:dw|
Dido525
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I got this far:
Dido525
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|dw:1353113577149:dw|
I am not sure if I can apply the fundamental theorem of Calculus here...
Dido525
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@zepdrix @TuringTest @AccessDenied
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I believe that you can apply the Fundamental Theorem of Calculus here if you take the derivative of both sides with respect to x.
Dido525
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of both sides? why?
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Equality only holds if you do to one side what you do to the other. This holds true for differentiation as well
Dido525
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Right...
Dido525
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so I get:
1+ln(x)=-2xf(x^2)
Dido525
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I sub in 4 and solve for f(x) right?
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Yes, that's what I am getting as well.
I then note that f(x^2) = f(4) if x=2. So I would substitute in x=2 to find f(4)...
Dido525
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Right...
Dido525
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I get:
|dw:1353114453992:dw|
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Yep, looks correct to me.
If we wanted f(x) in general, we'd probably just substitute in \(x = \sqrt{u}\) so the x^2 inside f(x^2) cancels with the root, but it seems easier to just go directly from f(x^2). :)
Dido525
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Thanks a lot for helping me!
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You're welcome! :)