1-x² 1. The curve C has equation y = B (i) Express 1-x² 1+x² in the form A + where the values of A and B are to be determined. 1+x² (ii) Hence, find the exact value of the area of the region bounded by the curve C and the x-axis. 1+x²1

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A: Given, double integral J=∫-13∫02(x2-y2)2x+ydu dt  we can write it as : ∫-13∫02((x-y)(x+y))2x+ydu dt…

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A: Solution :-

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A:

Q: 4 Find the area of the region bounded by x = = 2y²+1 and the y-axis using the horizontal strip.

A:

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Q: (4)Let K be integer ring module 12 and let I=([4]) and J=([6]) be ideals of K. Then [2] belong to…

A: Given that, K=Z12 and ideals I and J are such that I=([4])=4Z12={0,4,8} J=([6])=6Z12={0,6} Now,…

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A:

Q: II. Minor and Cofactor 1. Find the cofactor of 6 in matrix D 9 8 4 2 7 -9 3 4 D = -3 2 3 9 3 2 6 8 ㅋ

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Q: Evaluate: ³₁¹[z³(x + y)³] dz dy dx

A: We have to solve given problems:

Q: 10 Consider A = {z € C : |2|< 1}. The complex line integral Jonate=2) dz equals: (A) 0 (B)-ni+e²/2…

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Q: 1. Identify the surfaces of the following equations by converting them into equations in the…

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Q: 5. If Evaluate the following. (a) F' (9) (b) F (0), by interpreting F (0) as an area 1) = ₂√25 - 1²…

A: We solve this using differentiation under integral sign. The detailed solution is given in the next…

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A: The limit of integration of the variable x varies from x=y13 to x=2. The limit of integration of the…

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A: For finding a zero of a function f, the secant method is defined by the recurrence relation.…

Q: Draw a direction field for the differential equation y' = −y(5 - y). Based on the direction field,…

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Q: An 11-m beam is subjected to a load, and the shear force follows the equation V(x) = 5 +0.25x² where…

A: We can solve this using given information

Q: 2. Evaluate the double integral that will find the volume of a solid bounded by z = 1-2y² - 3x2 and…

A: Solution :-

Q: Find the volume of the solid generated by revolving the region bounded by 2y = e-*², the x-axis and…

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Q: 3 The function f : R² → R defined by f(x, y) = x³ + y³ – xy, (x, y) € R², has (A) a saddle point and…

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Q: Problem 3. Let VCR³ be the region bounded by the planes z = 0, z = 1, and the surface defined by…

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Q: Find the General Solution of (D² + 5DD' +6D22)Z = 10 cos(x - y)

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Q: Find the area of the region bounded by x = and the y-axis using the horizontal strip. 2y²+1

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Q: 02u 0t2 = аг 02u ?x2

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Q: Find the common area enclosed by the polar curves r = 3-2 cose and r = 2. Zoom image 26.38 13.19…

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Q: ! (5) If f(x) Option 1 =.. Option 2 then f(x) is reducible in Z5 [x]. x² + 3 x² +1 x² + 2

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Q: Find the area of the region above the curve y = x2-6, below y= x, and above y=−x.

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Q: Evaluate the integral: ₁f2ef/³t Inu tans ds du dt 2е π/3. 't

A: To Find:∫-10∫e2e∫0π3 t lnu tans ds du dt

Q: 3 Find the area of the region bounded by 2x = y²+1 and the y-axis using the horizontal strip.

A: The given region is bounded by 2x=3y2+1 and the y-axis.

Q: 02u at2 = ә2u аг 0x2

A:

Q: A mass weighing 5 lb stretches a spring 9 in. If the mass is pushed upward, contracting the spring a…

A: Given information is weight  w = 5 lb And, mass m =wg =532  lb s2/ ft k= Fs 14 = 514 =20  lb/ft As,…

Q: Find the area of the region bounded by the curves y = (x+8)2 y = 4 and the x-axis using vertical…

A: To find the area of the region bounded by the curves y=1x+82, y=4and x-axis i.e. y=0 using vertical…

Q: 3. Let G be the solid region inside the sphere of radius 2 cen- tered at the origin and above the…

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Q: agram and shade the region for e ~B)]

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Q: Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis, and…

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Q: 5. Consider the permutations f 1 2 3 4 2 1 3 4 on the set {1, 2, 3, 4). (a) Find fog and go f. (b) F…

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Q: 1. Consider the ordinary differential equation = (1-x-¹)y, with the initial values x = 1, y = 1.…

A: According to rule of bartleby we can solve only first question or 3 subquestions of first question…

Q: f₁ = x² - 6x f₂ = x² + 6x f3=x²-3

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Q: The equation y = O A. y" - 3y + 10 = 0 O B. y" - 3y + 10y = 0 O C. y" + 2y + 10y = 0 O D.y" - 2y' -…

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Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

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Q: Find the area of the region bounded by the curves 1 y = y = 4 and the x-axis using vertical strip.…

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Q: II. Problem Solving/Proving. Show all complete solutions. 1. Show that V = M22, the set of all 2 x 2…

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Q: Evaluate t 2-32² and trigonometr

A: We have to find the volume of the solid bounded by z=1-2y2-3x2 and the xy plane. The volume of the…

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Q: Suppose 3.141516 is estimated using 3.141529. The relative error is (Answer must be in 7 decimal…

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Q: Consider the following two player bi-matrix game 19 19 6 7 12 A = 2 14 16 6 B = (1₂ 0 -10 21 -8 -5 1…

A: