1. Find the maximum and minimum values of f (x, y) = x² + 3y + 7 on the set R, where R is the region bounded by the line y = x - 2 and the parabola y = 4 – x² as shown in the figure below. Include the boundary in the set. y=2-x 0 R y=4-x^2

Q: Find the area bounded by the arc square root x + square root y = 7, the x axis, and the line joining…

A: Given curves are                                                   1x+y=7, y=0, points (16, 9) &…

Q: 3. Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x-2y+3=0 and y = 0.…

A: Given that,  R be the region bounded by y=4-x2 and 3x-2y+3=0 and y=0. (a) Divided  the region in two…

Q: Find the of the region bounded by the parabolas y – 6x = -x² and y + 2x = x² , area

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Q: consider the 2D ice cream topper with a delicious scoop of ice cream that is enclosed by y=6|x| and…

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Q: Find the total areas of the shaded regions

A: Consider the given graph.The given functions are y=x2-4 and y=-x2-2x Find the intersection point of…

Q: Let R be the region to the right of y = x² below y = -2x + 80 and above y = 2x + 48. You can see…

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Q: Q2) A) Graph the curve Y = x (x +5)(x-3) between the value of x [-5, 3], then find the area of the…

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Q: Find the area of the surface S defined by z = xy and x² + y² ≤ 3. (Use syntax like 2*pi/3)

A: (.)  Given ,  Area of the surface S defined by z=xy and x2+y2≤3 .   If  z=f(x,y) ∀ (x,y)∈R  the…

Q: Find the area of the shaded region given below. y = √√√=x+4 y = √√x + 4 neg y = x² + 4 x = y² -6y +8…

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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.

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Q: Show that the rectangle that has maximum area for a given perimeter is a square.

A: Given the rectangle. We have to show that the rectangle that has maximum area for a given perimeter…

Q: y = x? - x - 12, y = 0, x = -3, x = 3 y 10 10 10 10 5 -4 2 -4 -2 4 2 4 -5 - 10 10 -10 -10 Find the…

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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: calculate the area of the bounded figure from the graph of the function y = x²-1 and the axis Ox

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Q: AP is perpendicular to PB, where A is the vertex of the parabola y^2 = 4x and P is on the parabola.…

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Q: Sketch the region given by the set {(x,y) | -3<x<3}

A: Given: A set {(x,y) | -3&lt;x&lt;3} The graph for the set -3&lt;x&lt;3 is: