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## Homework Statement

https://dl.dropbox.com/u/64325990/Capture.PNG [Broken]

I'm not even sure where to start :O

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- Thread starter theBEAST
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- #1

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https://dl.dropbox.com/u/64325990/Capture.PNG [Broken]

I'm not even sure where to start :O

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- #2

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[tex]f(0+\Delta x,0+\Delta y)\approx f(0,0)+\frac{\partial f}{\partial x}(0,0)\Delta x+\frac{\partial f}{\partial y}(0,0)\Delta y[/tex]

This uses the gradient in the sense of

[tex]df\approx \nabla f\cdot(dx,dy)[/tex]

Though I'm sorting of putting together whatever notation comes to mind, so let us know if you have notes close to this but aren't sure how they relate, or any other questions.

- #3

Curious3141

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## Homework Statement

https://dl.dropbox.com/u/64325990/Capture.PNG [Broken]

I'm not even sure where to start :O

Start with the Fundamental Theorem of Calculus to work out [itex]\frac{\partial f}{\partial y}[/itex] and [itex]\frac{\partial f}{\partial x}[/itex].

For the latter, you might find it more helpful to switch the bounds and put a negative sign on the integral.

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- #4

SammyS

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You have received two very good tips.## Homework Statement

https://dl.dropbox.com/u/64325990/Capture.PNG [Broken]

I'm not even sure where to start :O

I'll make my response more concrete.

cos(t

Let G(t) be an anti-derivative of cos(t

Then of course, cos(t

Using this to evaluate your integral gives:

[itex]\displaystyle \int_{x}^{y}{\cos(t^2)}\,dt=G(y)-G(x)\ .[/itex]

Now take the gradient of that.

Can you take it from here?

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