QI) Evaluate . F dr, where F(x, y) = (x² + 1, y3 – 3y + 2) and C is the top half-circle from (4,0) to (-4,0).

Q: Find the length of the curve y = x³/2 from (1, 1) to (2, 2/2).

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Q: Using Lagrange multiplier, find the minimum value of f(x,y) = 3x +ly on the circle x2 + y2 = 1. Give…

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Q: Find the abscissa on the curve x²=2y which is nearest to a point (4, 1). А. 0 С.2 В. 1 D. 3

A: Use the distance formula then minimise using derivative.

Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

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Q: Or Using Green's theorem find the value of 6 F. dr Where F(x, y) = (2e-5x – y²)i + (y³ + 2x²)j and C…

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Q: 10 Given: Y is the midpoint of XZ Y Prove: XY = XZ Reasons

A: Since, you have posted multiple question. We will solve the first question for you. If you want any…

Q: 4.) y = VT, y = 3, x = 0 around the y axis %3D

A: Given, y = x1/2, y = 3, x = 0, we have to find the volume by rotating about the y-axis.

Q: 2. XY has an endpoint X at (2,– 4). If the midpoint of XY is (– 3,– 1), what are the coordinates of…

A: The midpoint of two points and is given by: where are coordinates of the midpoint.

Q: Find the points on the cone z = x² + y that are closest to the point (-3,-2,0) %3D

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Q: ) Find the Extreme values of f (x, y) = x³ + y² on the circle x² + y² = 1. %3D

A: To find the extreme values of the function f(x, y) =x3 + y2  on the circle which is the…

Q: Find the length of the curve y =/2 from z = 0 to z = 3. %3D

A: Integration of (1+(f'(x))2)1/2 form 0 to.3

Q: The set of points P(x, y) such that their distance from (3, 0) is v2 times their 1. distance from…

A: The   distance from point Px,y  to 3,0 is 2 times the distance from point Px,y  to 0,2. Solution:…

Q: Sketch a contour diagram for f(x, y) = x2 − 2y2 with three labeledcontours.

A: To sketch the contour diagrams for the given function of two variables

Q: Find the midpoint of these two points (4, 6) and (7, 10) Use the formulas: x = (x1 + x2)/2 %3D y (yi…

A: Consider the points, 4,6      and         7,10 The midpoints of two points is given by the formula,…

Q: Verify Green's Theorem where F1=y^2-7y , F2=2xy+2x and the curve C is a circle x^2+y^2=1

A: Given: F1=y2-7y , F2=2xy+2x and C is a circle i.e., x2+y2=1 As, we have:…

Q: Jategrate h (x.y) = (x+y)i+(-x)j over the closed curve that begins at (-1, 0), goes along the x-axis…

A: we will use green theorem here to solve this question

Q: Find the exact length of the curve. y2 - 16(x + 4)3, Osxs 2, y > 0

A: The given equation of the curve is y2=16x+43, 0≤x≤2, y>0. The graph of this curve in the interval…

Q: 8., (x + y) dA, where R is the region that lies to the left of the y-axis between the circles x? +…

A: As you have asked to answer question 8, we will answer question 8.Question 8.The given integral…

Q: b) Find the shaded area of diagram that shecked by curve y =x² + 2x and the line y

A: The area between curves y=f(x) and y=g(x) on an interval [a, b] where f(x)≥g(x) on the interval is…

Q: Q5. Prove that the circle {(x, y), x² + y² = 1} is not homeomorphic to the interval [-1, 1].

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: Eliminate the parameter to obtain an equation in x and y: x=-2cos2t, y=-2sin2t

A: x=-2cos2t y=-2sin2t using trigonometric property,               sin2t+cos2t=1

Q: Evaluate |-y dx+x dy , where C consist of the curves along the horizontal line from (-4,4) to (-2,4)…

A: The given integral is: ∫C -ydx+xdy Where C consists the curve along the horizontal line from -4,4 to…

Q: Find the length of the curve. t,0stsV3 The length of the curve x = t°, y= ť on 0sts 3 is (Type an…

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Q: Calculate both sides of Green's Theorem when F = [-x²y, xy²] and y positively oriented circle x2 +…

A: According to the given information it is required to calculate both sides of the Green’s theorem.…

Q: dz -, n = 2,3, 4, ... where z = a is inside the simple closed curve C. (z – a)" Evaluate

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Q: Find the points on the cone z 22 x2 + y? that are closest to the point (-5,2,0)

A: Find the points on the cone z² = x² + y2 that are closest to the point (-5,2,0).

Q: Use Green's theorem to evaluate ſ. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: We have to evaluate the integral ∫5xy+x2+y2dx+x2-ydy over the closed curve C. Comparing with…

Q: Find the exact length of the curve. y2 = 16(x + 4)3, osxs 2, y > 0

A: Given data:   The given expression is y2=16(x+4)3. The given limits of x is [a,b]=[0,2].   The given…

Q: 2 Find the points on the cone z = x´ + y´ that are closest to the point (2,-3,0)

A:

Q: Iz+ai| rupriants Prove that the equation Iz+2] = 5V13 the origin is distance from pror line and its

A: Prove that the equation z+2=z+3i represents a line and its distance from the origin is 51326.

Q: C is the part of the circle of radius 3 in the first quadrant from (3,0) to (0,3) and F = (1, -y),…

A: Given, C is part of circle of radius 3 in the first quadrant from (3,0) to (0,3) and F=[1,-y] The…

Q: Verify Green's Theorem for: f4y³dx-2x²dy where C, oriented anti-clockwise, is composed of the…

A: To find the integral ∮C4y3dx-2x2dy where C is the positively oriented closed curve x2+y2=9, y≥0 and…

Q: Find the points on the cone z^2=x^2+y^2 closest to the point (4, 2, 0).

A:

Q: Find the points on the cone z 22 = x2 + y? that are closest to the point (-3,1,0)

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Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

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Q: 7. Find the angle of intersection between the curves y = x + x-8 and y = x

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Q: Find the distance between the point (3,11,-2) and the plane X t 2y

A: Explanation of the answer is as follows

Q: 2. Let be the part of the circle x² + y² = 9 from (-3,0) to (0, 3) in the upper left quadrant.…

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Q: Find Ja xydx + sin(x)ydy, where C is the boundary of the triangle with vertices (0,0), (0, 1) and…

A: Let I is the value of given Line Integral.

Q: 5. Find the length of the curve y = 2(2+ x)², 1<x<8 %3D

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Q: Verify Green's Theorem in the plane for F = -3y³i+ (3x3 + cos y)j where C is the circle x2 + y? =…

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Q: Q5. Prove that the circle {(r, y), x² + y? = 1} is not homeomorphic to the interval [-1, 1].

A: Here we can prove this question using topological property connectedness.

Q: Find the maximum and minimum values f(1, y) = zy takes on the circle %3D r + y² = 12.

A: Lagrange multipliers method: First solve the following systems of equations: ∇fx,y=λ∇gx,y. The…

Q: Consider the region in the fourth quadrant between the circles x² + y² = 4 and x² + y² = 25 and…

A: answer is in next step. please give a like !!

Q: II. Find the acute angle between the given curves. 2. x'y+4a° y=8anx²=4 ay 3. x'y+4 y=8Ax*y=4

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Q: (2) find the (x,y) coordinates of all points of intersection ot the curves.

A: b.(2) Given the polar equation of two cardioids r=1+sinθ,r=1-cosθ. To find the points of…

Q: 23/ Find the angle between two curves: 3 y = 2 - x² , y = x²

A: The angle between two curves is given by the formula tan θ=f2'x0-f1'x01+f1'x0f2'x0 Given,…