Compute F. dr for the oriented curve specified. F(x, y, z) = (z³, yz, x), quarter of the circle of radius 2 in the yz-plane with center at the origin where y 20 and z 2 0, oriented clockwise when viewed from the positive x-axis

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

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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: Find the equation for the tangent plane at the point Po = (1,2, 2) on the surface x + 4y2 + 22 = 25.…

A: Equation of the Surface x2+4y2+2z2=25 point 1,2,2

Q: Find an equation for the tangent plane to the surface 22 – xy? = 0 at the point (1, 3, 3).

A: Given that At point (1,3,3) Take, Now to find the divergence of f, The divergence at point…

Q: Find an equation of the tangent plane to the surface z = x^3- y^2 + 12x + 2y at the point (1, 2, 5).

A: Given: z = x^3- y^2 + 12x + 2y (1, 2, 5)

Q: Compute F. dr for the oriented curve specified. Jc F(x, y) = (6, y), quarter circle x2 + y? = 1 with…

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Q: 1. Use the tangent plane to the surface f(x, y) = x² + y? mate f(1, 2). at the point P(-1,1,2) to…

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

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Q: Find an equation of the tangent plane to the surface given by z² – 2x2 – 2y? = 12 at the point (1,…

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Q: Set up an intergal of the Curve for the length 3T Y%3DZE* sin (x), O4 xE 2

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Q: Compute F• dr for the oriented curve specified. F(x, y) = (9, y), quarter circle x² + y2 = 1 with x…

A: Given:

Q: Find an equation of the tangent plane to the surface at the given point. z = x2 - 2xy + y2,  (2, 3,…

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Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y-xy= 0 2y+5x+x-x'y² =…

A: Find your answer below

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

A: We have to solve the given integral by Green's theorem.…

Q: Let C be the curve given by r(t) = (t cost,t sin t,t).(a) Show that C lies on the cone x 2 + y2 = z2

A: Consider the parametric equation of the curve C : rt=tcos t,t sin t, t. To show C lies on cone…

Q: Find an equation of the tangent plane to the surface z = x2 + y2 + 2 at the given point (1, 3, 12)

A: Given surface, So

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

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Q: 2. Prove that the following curves are intersecting with a right angle: 5y-2x+ y –x*y =0 2y+5x+x*…

A: Given curves are  5y-2x+y2-x2y=0and2y+5x+x4-x3y2=0

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: find the tangent plane to the surface z = y-x at the point (1,2,1)

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Q: Find an equation of the tangent plane to the given surface at 'the specified point. Z =2x²+y&-5y and…

A: The equation of a tangent plane to the surface f(x,y,z) at the point x0 , y0 , z0 is calculated…

Q: Compute F. dr for the oriented curve specified. F(x, y) = (9, y), quarter circle x² + y2 = 1 with x…

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Q: 9) Find a point on the surface z = 8- 3x2 - 2y2 at which the tangent plane is perpendicular to the…

A: In this question we have to find a point on the surface at which the tangent is perpendicular to the…

Q: Compute f ds for the curve specified. f(x, y, z) = xz, r(t) = (3e, 2v5t, 4e) for 0sts 1

A: Here the provided function f(x, y, z) of three variable and a curve C is defined. Then the line…

Q: Find the equation of the tangent plane to x² the surface z = + y? 4 - at the point (2, 3, 10) x + 6y…

A: The equation of the tangent plane to a surface f(x,y,z) is given by:

Q: Find the equation of the tangent plane to x2 the surface z = 4 + y? at the point (2, –2, 5)

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Q: Find an equation of the tangent plane to the surface z = -! -3x? + 3y – 2x + 2y + 2 at the point (2,…

A: We have to find tangent plane

Q: 4. Find both points on the surface xz – x2 – y? = 8 where the tangent plane is horizontal.

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Q: For the level curve f(x,y,z)=12 for f(x,y,z)= 4x2 − 2y2 + z2 at the point (2,2,2), find the…

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Q: 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…

A: Consider the given equation: And the plane x+y+z=9 centered at 4,3,2.

Q: 12. Find the area of the surface generated when the curve y = ,on [1,2] is rotated about the x-axis.

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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 the area of the surface generated when the given curve is revolved about the x-axis. y = V3x +…

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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 length of the curve y=z from z 0 to z=4.

A: The length of the curve is given by:

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

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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 area of the surface that is generated by revolving the portion of the curve y = x2 between…

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Q: Compute f ds for the curve specified. f(x, y, z) = x²z, r(t) = (3e*, 2/6t, 4e-t) for 0 sts1

A: Given:

Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y = /5x +…

A: To find the surface area generated when y=√(5x+3) is revolved around the x-axis on [0,5]

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 tangent plane to the surface at the given point. h(x, y) = In V x2 + y², (6,…

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Q: Compute F• dr for the oriented curve specified. F(x, y) = (9, y), quarter circle x² + y² = 1 with xs…

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Q: Find the equation of the tangent plane to the surface z = 4.x*y? + 2y at point (1, -2, 12).

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Q: 12. Find the area of the surface generated when the curve y =+,on [1,2] is rotated about the x-axis.

A: solution is given below...

Q: Find the slope of the tangent line to the curve that is the intersection of the surface z=x² - y…

A: The details solution is given below

Q: Find the angle of inclination of the tangent plane to the surface 3x2 + 2y2 − z = 15, at the given…

A: We have given surface 3x2+2y2-z=15 at point (2, 2, 5)   We have to find the angle of inclination…

Q: Find the equation of the tangent plane to the surface z = +y? at the point (2, –2, 5)

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