Dx dy where R is the unit circle.

In summary, "Dx dy" is a notation used to represent infinitesimal changes in the x and y coordinates of a point on the unit circle. It is not directly related to the radius of the circle, and it is not used to find the circumference or area of the circle. However, it can be applied to other shapes besides the unit circle in various mathematical equations and functions. It is commonly used in calculus to represent the slope of a curve at a specific point.
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Given the double integral [tex]\int\int_R[/tex] [tex]\sqrt{}x^2+y^2[/tex] dx dy where R is the unit circle.
We are only given the equation for the unit circle but don't we need more equations so I can change the equations to a single variable and then find the Jacobian so how do I find the Jacobian.
How do I find a point interior to R at which the Jacobian vanishes.
 
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1. What does "Dx dy" mean in the context of a unit circle?

"Dx dy" refers to the infinitesimal changes in the x and y coordinates of a point on the unit circle. It is often used in calculus to represent the slope of a curve at a specific point on the circle.

2. How is "Dx dy" related to the radius of the unit circle?

"Dx dy" is not directly related to the radius of the unit circle. It is used to represent the change in the coordinates of a point on the circle, while the radius represents the distance from the center of the circle to that point.

3. Can "Dx dy" be used to find the circumference of the unit circle?

No, "Dx dy" is not used to find the circumference of the unit circle. The circumference can be found by using the formula C = 2πr, where r is the radius of the circle.

4. How is "Dx dy" used in the equation for the area of a circle?

"Dx dy" is not used in the equation for the area of a circle. The area of a circle can be found by using the formula A = πr^2, where r is the radius of the circle.

5. Is "Dx dy" applicable to other shapes besides the unit circle?

Yes, "Dx dy" can be used to represent infinitesimal changes in the coordinates of points on any curve or shape, not just the unit circle. It is a commonly used notation in calculus and can be applied to various mathematical equations and functions.

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