Alevel math A set of curves that each pass through the origin have equations y=f1(x),

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interlanken-fall
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A set of curves that each pass through the origin have equations y=f1(x),f2(x) and f3(x) where f 'n(x)=fn-1(x) and f1(x) =x^2.

a) find f2(x), f3(x)
b)suggest an expression for fn(x)
thanks
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mqb2766
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(Original post by interlanken-fall)
A set of curves that each pass through the origin have equations y=f1(x),f2(x) and f3(x) where f 'n(x)=fn-1(x) and f1(x) =x^2.

a) find f2(x), f3(x)
b)suggest an expression for fn(x)
thanks
Have you tried integration?
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interlanken-fall
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(Original post by mqb2766)
Have you tried integration?
what do we integrate and why do we integrate ?
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(Original post by interlanken-fall)
what do we integrate and why do we integrate ?
Ghostwalker explained it fairly clearly on the other thread.
You know the derivative, so integrate to get the curve.
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interlanken-fall
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so the
derivative is the rate of change, and so because its x2 then we integrate it to get the equation from it? how do we do that for f2(x) and f3(x) do we multiply by 3 or? do we integrate evern further
(Original post by mqb2766)
Ghostwalker explained it fairly clearly on the other thread.
You know the derivative, so integrate to get the curve.
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(Original post by interlanken-fall)
so the
derivative is the rate of change, and so because its x2 then we integrate it to get the equation from it? how do we do that for f2(x) and f3(x) do we multiply by 3 or? do we integrate evern further
Have you worked out f2 by integrating f1?
If so, what did you get?
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interlanken-fall
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(Original post by mqb2766)
Have you worked out f2 by integrating f1?
If so, what did you get?
by integrating X2 i get = x^3/3
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interlanken-fall
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(Original post by interlanken-fall)
by integrating X2 i get = x^3/3
and for f3(x) I integrate again = 1X^4/12
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interlanken-fall
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I just dont understand why we integrate
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(Original post by interlanken-fall)
I just dont understand why we integrate
Because you're told the
* Derivative of f2 is f1. So integrate (inverse of derivative) to get f2.
* Derivative of f3 is f2, so integrate (inverse of derivative) to get f3
..... And so on ...
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(Original post by mqb2766)
Because you're told the
* Derivative of f2 is f1. So integrate (inverse of derivative) to get f2.
* Derivative of f3 is f2, so integrate (inverse of derivative) to get f3
..... And so on ...
omg you are amazing and a genius thank you!!!!!!!
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