Consider calculating the size of the region N:= {(x, y) E R² : y > v3x², æ² + y² < 4} , with the 2d integral, Sl, dædy.

Q: suppose A is a positive real number, determine the area of the traingle enclosed by the lines x=0,…

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Q: Find the area bounded by the following curve and line: y=4/x , y²-4y+2x=5 and the line y=4

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Q: 5. Determine the point intersection between curve y= x(3-x)and the line y= x. Hence, find the area…

A: To find the intersection points of the given equations y = x(3-x)  and y = x

Q: Find the average squared distance between the origin and thepoints on the paraboloid z = 4 - x2 -…

A: Given: Paraboloid: z=4-x2-y2, z≥0 To find the Average squared distance.

Q: #7. Describee the area represntecl by lin in n-1

A: L'Hospital's rule:

Q: hat is the area of the region bounded by the line x = 4 and the curve x³ = x² + 2xy - y² = 0. ht:…

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Q: Q2) Find the area between a curve y-x+1 and the line y-2-xx≥ 0. AMP

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Q: 2. For F = (xz3, 2y*x²,5z?y) find: a. div F b. Curl F and find div(curl F) C.

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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 surface area for the object obtained by rotating y = 7x + 2 about the x-axis over the…

A: The object is obtained by rotating about the x-axis over the interval .We have to find the surface…

Q: Real mathematical analysis proof : If x, y are non-negative real numbers, prove that x + y = y + x…

A: We have x, and y are non-negative real numbers. We have to prove that x+y=y+x and x·y=y·x.

Q: (b) the curve x = = y²-y-6 and the line x = = 2y + 4;

A: Given; x=y^2-y-6, x=2y+4

Q: Ray AB bisects CAT. If mLCAT= 30 and mL CAB= 2x + 10 then give the value of x.

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Q: Make two separate plots of the function z - 2 sin (1.5x) in the domain -3sxs3 and -3Sys3. 3-D…

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Q: A) Give f(x)-V-3 find f-*(x) ,x >0 B) : Find the area bounded by the curve y = f(x) =v2x +1 and the…

A: We have to find  A) f-1(x) for f(x) =√(x-3)  B) area bounded by the curve y = √(2x+1) and the lines…

Q: 3. Find the centroid of the area bounded by the curves y = x³ and y = √x.

A: The area is bounded by the curves y=x3 and y=x. We have to find a centroid.

Q: ). Explain how we get the Cylinder by equivalent relation.

A: Please check the next step for details

Q: Find the area between the curve of y ਆਗੂਆਂ 2 4 = zæ + 2 and the x-axis on the interval [-2, 1].

A: Given that , Now we want to find the area between the curve and the axis  on the interval .

Q: 1. Find the total area bounded by the curves y=x²-3x and y = x³ + x² −12x.

A: Given curves are y=x2-3x y=x3+x2-12x Take  y=fxHere,   fx=x2-3x y=gxHere,   gx= x3+x2-12x

Q: Using the extended CIF compute: (Justify your steps! iv) { 2 (1-2jadz - C is a simple, closed,…

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