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with all steps shown? 5. Let A be the inside and boundary of the triangle in R2 whose vertices are (0,0), (1,0) a...
Let A be the inside and boundary of the triangle in R2 whose vertices are (0,0), (1,0) and (0,1). Let C be the curve obtained by proceeding around the boundary of A in an anti- clockwise direction. P...
Let A be the inside and boundary of the triangle in R2 whose vertices are (0,0), (1,0) and (0,1). Let C be the curve obtained by proceeding around the boundary of A in an anti- clockwise direction. Prove İ}!").lx (ly İ)(2 dr dy. Pdr+Qdy That is, prove Green's Theorem for the triangle A. [Hint: the lecture notes have a proof for when A is a rectangle. So, the idea is is to give a similar proof where we have this...
3. Let S be the triangle with vertices at (0,0), (1,0) and (0,1). Let f (x,...
3. Let S be the triangle with vertices at (0,0), (1,0) and (0,1). Let f (x, y) = e***. Use the change of variables u = x – y, v = x +y to find . f(a,y) dA.
Done Expert Q&A 5. Let A be the inside aad boundary of the trigl in ioes are (0,0). (1.0) and (0.1). Let C be t...
Done Expert Q&A 5. Let A be the inside aad boundary of the trigl in ioes are (0,0). (1.0) and (0.1). Let C be the eurve obtined bey peoceeding and the omday of A in an elockwise directicn. Prove when A is a rectangle. So, the idea is is to give a simlar peool we we have this triangk A in place of a rectang 3 marks End of qaestons
Done Expert Q&A 5. Let A be the inside aad...
5 ve 6. Soru Dry - xdA over the triangle with vertices ( -1,0), (0,0) and...
5 ve 6. Soru
Dry - xdA over the triangle with vertices ( -1,0), (0,0) and (0,1) changing the variables by u = y - x and v = y + x. (DONOTEVALUATE INTEGRAL) 1 w 5. (15 points) Write the integral representing the area of the region al < x2 + y2 < band below the line y = x in polar coordinates.(DONOT EVALUATE INTEGRAL) ,y,z) as an iterated integral in cartesian coor- dinates. E is the region inside...
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector...
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector field F conservative? If so, find a potential function, and use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the vector line integral ScF. dr along any path from (0,0,0) to (1,1,1). 6. Compute the Curl x F = Q. - P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) $ex* dx +...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
Let A be the inside and boundary of the triangle in R2 whose vertices are (0,0), (1,0) and (0,1). Let C be the curve obtained by proceeding around the boundary of A in an anti- clockwise direction. Prove İ}!").lx (ly İ)(2 dr dy. Pdr+Qdy That is, prove Green's Theorem for the triangle A. [Hint: the lecture notes have a proof for when A is a rectangle. So, the idea is is to give a similar proof where we have this...
3. Let S be the triangle with vertices at (0,0), (1,0) and (0,1). Let f (x, y) = e***. Use the change of variables u = x – y, v = x +y to find . f(a,y) dA.
Done Expert Q&A 5. Let A be the inside aad boundary of the trigl in ioes are (0,0). (1.0) and (0.1). Let C be the eurve obtined bey peoceeding and the omday of A in an elockwise directicn. Prove when A is a rectangle. So, the idea is is to give a simlar peool we we have this triangk A in place of a rectang 3 marks End of qaestons
Done Expert Q&A 5. Let A be the inside aad...
5 ve 6. Soru
Dry - xdA over the triangle with vertices ( -1,0), (0,0) and (0,1) changing the variables by u = y - x and v = y + x. (DONOTEVALUATE INTEGRAL) 1 w 5. (15 points) Write the integral representing the area of the region al < x2 + y2 < band below the line y = x in polar coordinates.(DONOT EVALUATE INTEGRAL) ,y,z) as an iterated integral in cartesian coor- dinates. E is the region inside...
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector field F conservative? If so, find a potential function, and use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the vector line integral ScF. dr along any path from (0,0,0) to (1,1,1). 6. Compute the Curl x F = Q. - P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) $ex* dx +...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
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