Find F. dr where C is a circle of radius 2 in the plane. x+y+z 9, centered at (4, 3, 2) and oriented clockwise when viewed from the origin, if F = 2yi – 4xj + 2(y – x)k

Q: Find an equation of the tangent plane to the surface at the given point in the figure below.

A: The function of the given surface can be written asG(x,y,z)=ln1+4x2+9y4-0.1z2Find the partial…

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Q: If (a,ß.r) is a point at which the surface x2+y2-z-2x+42=0 has a horizontal tangent plane, then Iyl=

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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: Н.W Ql: Evaluate f y* dx - x'dy where C is the positively oriented circle of radius 2 centered at…

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Q: Let F = (5e**+1 + y)ï + (2x – sin(3y – 2))j and C be the boundaries of the circle x? + (y – 2)² = 4…

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

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Q: z = In (x² + y²) at point Po(1,0, 0).

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Q: Find F. dr, where F = 3yi – 8x3+ (8y – 8x)k and C is a - circle of radius 8 in the plane x + y + z =…

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Q: The curve C is the circle of radius 5 contained in the plane z 5 and centered around the z-axis,…

A: Solution:-

Q: Which of the following is the equation of the tangent plane to the surface z = 3x2 +x-y²+y at the…

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Q: Consider the curve C shown in the attached figure, which is the intersection between surfaces S, and…

A: To parameterize the curve which is the intersection of the below curves in the first octant.…

Q: 4. Let C be the unit circle in the xy-plane, and S be the boundary of the square with side 1,…

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Q: Find the area of the surface generated when the given curve is revolved about the y-axis. y-(3x)13,…

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Q: Find the equation of the tangent plane to the surface z = 4 +y? at the point (2,-3, 10) Ox+ 4y- z =…

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Q: If (a,B.y) is a point at which the surface x2+y2-z²-2x+12=0 has a horizontal tangent plane, then y|…

A: As per guidelines, we will solve first question only. Let α,β,γ be the point on the surface…

Q: If (a,B,y) is a point at which the surface x-+y²-z²-2x+12=0_has a horizontal tangent plane, then…

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Q: 2) Consider the oriented curve C given by C = C1uC2, where C2 is obtained by intersecting the…

A: We will first parametrize the curves C1 & C2 then substitute the x,y,z values into the line…

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² – 2xy + y²,…

A: Given problem:- Find an equation of the tangent plane to the surface at the given point. f(x, y) =…

Q: Find an equation of the tangent planes to the given surface at the specified point. (a) f(x,y)= 4x…

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question.

Q: Find the area of the surface generated when the given curve is revolved about the x-axis. X₁ 1 y=6 1…

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Q: Find F. dr where C is a circle of radius 3 in the plane x + y + z = 6, centered at (1, 3, 2) and…

A: Given  Radius of circle r=3Equation of plane x+y+z=6

Q: ) Find the gavea d the rgion enclased by the line x-In3 and the curves y= ex and y=ex

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Q: Find . F.dr when F(x,y) = (2x,3y²) and C is only the first quadrant part of a circle of radius 3…

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Q: Find the tangent plane to the surface z = 9 – x* – y? at the point (1, -3, –1).

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Q: Find the tangent plane to the following surfaces at the point (1, 2, 3): a.) z = x + y     b.) z + 2…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² – 2xy + y²,…

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Q: Find the extreme values of the function ƒ(x, y, z) = xy + z2 on the circle in which the plane y - x…

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Q: Find the area of the surface generated when the curve f(x) = (2/3)x^(3/2) - (1/2)x^(1/2) ; [1,9] is…

A: Given:

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A: Given function is, z=lnx2+y2

Q: |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: Find the equation of the tangent plane to the surface of the equation z = x2 + y2 - 2xy on the point…

A: Equation of tangent plane

Q: Find the extreme values of the function f(x, y, z) = xy + z^2 on the circle in which the plane y - x…

A: Given function is fx,y,z=xy+z2. We have to find the extreme values of the given function on the…

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: Find an equation of the plane tangent to the following surface at the given points. 元 z= 4 cos (x-…

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Q: (b) Consider F(x, y) = -i+ j, where (x, y) # (0, 0). x²+y2 x2+y2- Without using Green's Theorem,…

A: Consider the provided function,

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In V x2 + y², (6,…

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Q: If (a,B,y) is a point at which the surface x²+y²-z²–2x+104=0 has a horizontal tangent plane, then…

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Q: Find fa F. dr where C is a circle of radius 1 in the plane x + y + z = 3, centered at (1, 3, -1) and…

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Q: (a) Find the area of the surface generated by the given curve about x-axis y = Vx , 18 x< 4

A: Note: According to Bartleby guidelines; for more than one question asked only the first one is to be…

Q: EVALUATE § 7. d² USING STOKE'S THEOREM 3xz^ + ex² ₁ + 2xy^ с F(x, y, z) = 3XZ1 te C IS THE CIRCLE…

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Q: Find the equation of the tangent plane to the surface x?+ Qy?-322=3' at (2-1,1) x²+ 2y 2-322=3'at…

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Q: Find an equation for the tangent plane to the surface z = 3y^2 − 2x^2 + x at P(2, −1, −3). Express…

A: Let's find equation of tangent plane.

Q: Find the area of the surface generated when the given curve is revolved about the x-axis.  y =…

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Q: Use Green's theorem to find the k number that satisfies (k + 3) ∫C((k/2)*(x^k)*(y^2))dx + ((yx^(k +…

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Q: -8x If the infinite curve y = e8x, x 2 0, is rotated about the x-axis, find the area of the…

A: Given curve is y=e-8x, x≥0 is rotated about x axis.

Q: Find the equation of the tangent plane to the surface z =e/ In (2y) at the point (2, 4,1.643). Note:…

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Q: Which of the following is the equation of the tangent plane to the surface z=x2 - x+3y² +y at the…

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Q: 7. Find the area of the portion of the plane z = 2y that lies directly above the circle x +(y-1)² =1…

A: we have to find area of the portion of plane .and coverting the problem in polar coordinate makes it…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.