Q2 Calculate 8- z dz, z(4 - z) where C is the circle of radius 7, centre 0, negatively oriented.

Q: Find the area of the surface generated by revolving the curve = V¤ + 3, 4 < y <7

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Q: Sketch the section of the surface at x = 0. y? – 42? = 4

A: Given

Q: Find the surface are generated when y= (x^3)/5 is revolved about the x axis on the interval…

A: Explanation of the solution is given below...

Q: The area of the surface obtained by rotating the curve y = 1sxse about the line x = 42 is

A: Given that y= 1/x  + x3 /12 and find the surface area. Here i attached solution of this question.

Q: (b) Find the circle of curvature at (0, 1)of the curve y = x3 + 2x² + x +1

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Q: Integrate f(z) = 1 Z³-Z4 clockwise around the circle C: |z| 1 NIT 2

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Q: 10. Evaluate , (2x – y) dA where D is bounded by the circle with center the origin and radius 2.

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Q: Find the area of the segment of a sphere formed by revolving the graph of       y = √(r2 − x2) , 0 ≤…

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Q: Find the curvature k of the circle C : (x – 2)² + (y + 3)² - at the point (5, 1).

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Q: Find the area of ​​the rotating surface that occurs by turning circle x2+y2=4 around line x=2 .

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Q: 35. In the xy-plane, the circles with equations (x-3)² +y² = 11. and (x+2)² + y² = r² |3D %3D 2re…

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Q: find the Volumae of soliel generated by revolving the region in the first quadsant bonended by y=X…

A: The volume of revolution generated by full revolution of the area A between the curves y1=f1(x) and…

Q: Find the area of the surface generated by revolving the curve about each given axis. x= 5t, y- 9t,…

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Q: e2z Evaluate a dz, where C is a circle with (z+1)* centre at origin, |z| = 3.

A: Given integral is ∮Ce2z(z+1)4dz Where C is  |Z| = 3

Q: Sketch the surface given by the function. z = 9-x?-y?

A: Given, z=9-x2-y2

Q: dø What is the curvature of the circle, x2 + y2 = 36 ? hint: k = ds change in angle of circle change…

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Q: Sketch the section of the surface at y= 0. 4. + 9 36

A: Given the equation4x2+9z2=36

Q: Find the curvature k of the circle C: (T – 2)² + (y + 3)² = 25 at the point (5, 1).

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Q: Please evaluate (3y – einl2) dr + (7x + V yt + 1) dy, where C is the circle x² + y² = 9. Hint: use…

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Q: What is the shortest distance from the surface xy +12x +z^2 =144 to the origin?

A: To find the shortest distance from surface xy +12x +z2 =144  to origin.

Q: 6y dA, R is the quarter-disk in the fourth quadrant enclosed by the curves r+ y = 16, r = =0, and y…

A: Explanation of the answer is as follows

Q: Find the areas of the surfaces generated by revolving the curve x= 2sqrt(4-y), 0≤y≤15/4

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Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is Then x…

Q: Consider the region left half-plane (that is, æ < 0), inside the circle x² + y? : and y = -6x .…

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Q: Q2 Calculate 8-る dz, where C is the circle of radius 7, centre 0, negatively oriented.

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Q: Find the surface area of the cone frustum generated by revolving the line segment y = 4 1 over 1 < x…

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Q: F = (y + 2x, 2x + 5z, 1y + 8x), C is the circle with radius 5, center at (2, 0, 0), in the plane x =…

A: F=y+2x, 2x+52, 7y+8xCircle centered at (2, 0, 0) and radius is 5In x=2 planeOrientation- counter…

Q: Find the area of the surface formed by rotating the curve with the equation x ^ (2) - (y ^ (2)) /…

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Q: (d) Find the area of the surface generated by revolving the curve y = 2a, 0 < x < 3, about the…

A: Part (D) To find the area of the surface generated by revolving the curve, y=2x,0≤x≤3, about the…

Q: How many square units is the area of the surface obtained by rotating the curve y = V4-z, 0 <I<2…

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Q: Show that the curve given by, R(t)=(2sint)i+(2sint)j+(sqrt(8)cost)k lies on a sphere centered at the…

A: The equation of a sphere, centered at h,k,l, is defined by the equation, x-h2+y-k2+z-l2=r2 , where,…

Q: Evaluate |*(x + 7) – 2y ds where C is the circle of radius 1 centered at (-3,0) and lying on the…

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Q: Determine the osculating circle of the helix defined by y = x^3 − 3x + 1 at x = 1.

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Q: ⒸFind S (x- y²) dA, where I is bounded by the circle of D center (0,0) and radius 2.

A: As per as our guidelines i am supposed to answer

Q: Find the curvature k of the circle C : (x – 2)² + (y+ 3)² 16 at the point (2, 1).

A: Use the formula of curvature to solve this problem.

Q: Find the area of the surface obtained by rotating the circle x^2+y^2=r^2 about the line y=2r

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Q: Consider the line L = {z = x + iy e C, y = 1} Let C = {w 1 -, z € L} with Convince yourself that C…

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Q: Find the length of the circle of radius r defined parametrically by x=rcost, y=rsint,0≤t≤2π.

A: Here I am attaching image so that you understand each and every step.

Q: Integrate counterclockwise dz, C' the circle with z² + 8z + 15 center -3 and radius 2. dz = La z2 +…

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Q: Find the curvature K of the circle C: (x - 2) + (y+3)² = 16 %3D at the point (2, 1).

A: Given: Equation of circle C: (x-2)2+(y+3)2=16 ⇒ (x-2)2+(y-(-3))2=42 We know that circle equation is…

Q: Find the area of surface that is generated by revolving the portion of the curve x = /9 – y? , -2 <…

A: We will find out the surface area of revolution.

Q: Q2 Calculate dz, - z) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A: Since you have asked multiple questions here, we will solve the first one for you. To get the…

Q: Calculate 8-2 dz, z(4 – z) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: Find the exact area of the surface obtained by rotating the curve abo = V7 - x, 1<x< 7

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Q: Evaluate the double integral. (8x – 6y) dA, D is bounded by the circle with center the origin and…

A: The given data is: ∫∫D8x-6ydA To evaluate the double integral.

Q: 2. Write the equation of the circle with Center (-1, – 8) and Radius : V7 x2 + 2x + y? + 16y + 58 =…

A: Topic-analytic geometry

Q: Find the area of the surface generated by revolving the curve about each given axis. x = 6t, y = 9t,…

A: Here,  we need to find the surface generated by revolving the curve x=6t, y=9t, 0≤t≤3, about each…