Find the area of the part of the plane z=3x+5 y+3 that lies above the region R=(x,y) 2≤x≤3; 1sys5.

Q: Find the area of the shaded region. y-2 C4, 2) O4, 2 A) 2 (B) n-2 D) n

A: The area of the region can be found by the following formula  Area =∫abydx Area =∫ab|f(x)-g(x)|dx…

Q: Sketch the surface 1≤z≤ √9-x² - y² 1≤z≤√9-x² - y² and_x² + y² ≤1

A: Given is the surface surface 1≤z≤9-x2-y2 and x2+y2≤1 The objective is to sketch this surface.…

Q: S SR (4x + 8y)dA, where R is the parallelogram region with vertices (-1,3), (1, −3), (3, −1) and…

A: To Evaluate: Where, is the parallelogram with vertices . Transfomations: ,

Q: Q2: f(x. y)- x/y over the region in the first quad- rant bounded by the lines y x,y 2x,x 1,x-2

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Q: EX Find the region-in the Z-plane represented by

A:

Q: Let R be the rectangular region with (1,2) , (2,3) , (3,2) and (2,1) as corners. Use change of…

A: Changing the variables

Q: 1 Set up and evaluate , 6x dA, where R is the rectangular region with corners (-2, 0), (3,0), (-2,…

A:

Q: Find the area of the cap cut from the paraboloid y^2+z^2=2x by the plane x=2

A: To Find: Area of the cap cut from the paraboloid y2+z2=2x by the plane x=2.

Q: Sketch the surface 1≤z≤√√9-x²-y²_and_x² + y² ≤

A: Solution is below

Q: y = 2x2 + x - 6 y= x² - 4 y 5- (2, 4) 4+ 3+ 2+ 1+ + + -3 -1 -1+ 1 X -2+ -3+ -5 -7+ 3.

A:

Q: Find the area of the region included between the parabolas y² = 4(p+1)(x + p + 1), and y² = 4(p² +…

A: As per the question we are given two parabolas defined as : P1  :  y2 = 4(p+1)(x+p+1) P2  :  y2 =…

Q: The area D is the area in the XY-plane bounded by the X-axis, Y-axis, and the 4x + line 5y = 0.…

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Q: 19. y² dA, D is the triangular region with vertices (0, 1), (1, 2), (4, 1)

A: 19. Given D is the triangular region with vertices (0, 1), (1, 2), (4, 1).We find the given double…

Q: Q2 where R is the region bounded by y =x and y = 2vx

A:

Q: Shade the area of the region bounded by the parabola, x 2+p2-2(p+7)x-5y+59 + 14p 0 and the straight…

A: Equation of the parabola: x2 + p2 -2p+7x - 5y + 59 + 14p = 0               (1)Equation of lines:x =…

Q: Find the points on the cone 2 = r² + y? that are closest to the point (4, 2, 0). (Hint: You can…

A: Here we use the distance formula  D=(x2-x1)2+(y2-y1)2+(z2-z1)2 where D is the distance between the…