3 3 Use the transformation u = 3x + 4y, v = x + 3y to evaluate the given integral for the region R bounded by the lines y = -x +3, y = -x --x+4, 4 1 1 y = -x, and y = -x + 3. R (3x² + 13xy + 12y²) dx dy (3x²+ 13xy + 12y²) dx dy = ¯ R (Simplify your answer.)

Q: find the residues of z/(1-z^4) at z = i

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Q: State the area of the region, determined by the lines, y = 14x, y = 4x + 2, y = 14x – 4, y = 4x + 7…

A: we know we will use jacobian to transform the change of variables here .

Q: State the area of the region, determined by the lines, y = 6x, y= 4x +2, y = 6x – 5, y= 4x + 4 with…

A: Let D denote the given region.

Q: Find div F and curl F if F(x, y, z) = x³i - 10j+yzk. div F= curl F=

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Q: 2 y = 12 – 3x", y = 4 – x 2

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Q: Integration of( 3x2-3yz+2xz)dx + (3y2-3xz+z2)dy + (3z2-3xy+x2+2xz)dz along straight line joining…

A: Given: ∫-13∫22∫31(( 3x2-3yz+2xz)dx + (3y2-3xz+z2)dy + (3z2-3xy+x2+2xz)dz )

Q: If R is the region boundeb by the square a|+|y = 1 then ffR(y-2)dA is equal

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Q: Let E be the region inside the graph of +E + z? = 1. Use the transformation x = 3pcos(0) sin($), y =…

A: We will use coordinate to solve the following question

Q: True or fulse

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Q: Find div F and curl F if F(x, y, z)=xi - 10j+yzk. div F= curl F=

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Q: 2 y = 2x – x¯, y = 2x² – 4x

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Q: ind the area of the region bounded above by y O O पं ထာ 16 3 -2. 32 3 O 36 4 X = —2 + 5 and below by…

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Q: ·볼+1 2x - y dx dy, Use the transformation to evaluate 2x-y where u = v = % and integrating over an…

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Q: Which of the following integral is the integral f f, el+s)/(c~-3) dA where Ris the trapezoidal…

A: To   sketch the region R   and choose an appropriate change of variables          for the…

Q: Find the global min and max of the provided function on the provided region R: f(x,y) = x - y - xy…

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Q: State the area of the region, determined by the lines, y = 13z, y = 2z + 2, y = 13z – 4, y = 2x + 7…

A: we will use transformation and jacobian here.

Q: use the lagrange multiplier to find extreme points of f(x,y,z) = 2x+z over the intersection of…

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Q: Map the image of Ay=x^(1/2) on the w- plane of transformation w=B *Z^2 Assume all missing or error…

A: Given: Now the given are, On the w-plane of the transformation w=B *Z2, map the image of…

Q: Evaluate the integral 108 - 2y/E+ 4ydzdy, 4 where A is the parallelogram with vertices (0,0), (),…

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Q: Plot the function f(x, y) = x² – y² over the square region bounded by the lines y =x - 2, y =x+ 2, y…

A: Given the function fx,y=x2-y2

Q: Which of the following mappings does not define a linear transformation A: R^3 -> R^2?

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Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: Write the integral that can be used to find the region bounded by x = -3y² + 4 and x = y³.

A: We have to construct  the integral to find the region bounded by given curves.