Sketch the portion of the surface that lies in the first octant: y = z. 0.15 0.a 0.1 0. 0.15 0.18

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

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Q: Graph the curve 8y2 = x2 (1 − x2 ). Use a computer algebra system to find the surface area of the…

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Q: (b) Sketch the trace of the surface z = 2x? – y? when x = -1. Label your axes, and give the…

A: Given surface is  z=2x2-y2          (i) By putting x=-1 in (i), the surface becomes z=2-y2 The graph…

Q: Find the area of the surface generated by revolving the curve about the (a) x-axis and (b) y-axis.…

A: Explanation and solution is given below....

Q: Find the area of the surface generated by revolving x = t+2/3, y = +2/3t+3, -2/3 sts2/3 about the…

A: The surface area of disk is s=πr2 h  where r is radius and h is width

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 4x = y? + 20,…

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Q: a. Find the area of the surface generated by revolving about the x-axis the loop of the

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Q: Find the surface area of the torus obtained by rotating the circlex 2 + (y - b )2 = r 2 about the…

A: Given the equation of the circle  x2+(y-b)2=r2. We need to find the surface area of the torus…

Q: Find the surface area of the portion of the sphere generated by revolving the curve y = 1- x, 0 <xs;…

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Q: Find the area of surface that is generated by revolving the portion of the curve 9 – y² , – 2 < y< 2…

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Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y? + Z?…

A: We need to identify a generating curve on the xz-plane for the surface of the revolution with the…

Q: Sketch the portion of the surface that lies in the first octant: x = y. 12 1.5 1 0.5 0.15 . 0. . 2.

A: The given plane is in first octant and the plane is given by:  x = y

Q: Sketch the surface created by 4.r2 + 9y? + 3622 = 36. %3D

A: Given,4x2+9y2+36z2=36 Simplify equation (i) as x29+y24+z21=1  .....(i) Intercepts along x,y,z…

Q: Use traces to sketch and identify the following surface 25x² + 4y? + z² 100.

A: Given: The surface 25x2+4y2+z2=100.

Q: Find the exact area of the surface obtained by rotating the given curve about the y-axis.

A: Given that      x(t)=3t-t3y(t)=3t2 Since, we are rotating about y-axis, the formula is:…

Q: Determine the surface area generated by revolving the line segments about y-axis. 3m 4m 2m 1m 2m 2m…

A: Given , Line segment revolve around y-axis , we have to find surface area of formed shape .

Q: Identify and sketch the section of the surface at x = 0. 2y? – x + 22 = 50 Type of the surface:

A: This question is related to conic section .solve in step 2.

Q: Determine the area of the surface generated by rotating around the "y" axis, the curve described by:

A: Here, the given parametric curve is: x=t33, y=t+1; 1≤t≤2⇒x'(t)=t2, y'(1)=1 Now, the surface area…

Q: Find the surface area of the plane ( 15x- ? 5z+20y=D35) if it is in the first octant

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Q: Q4(a) Find the area of the surface generated by revolving the curve, x = /6y – y2 ; 2<y<5

A: Given the curvex=6y-y2    , 2≤y≤5we need to find the area by revolving the curve about y axis from…

Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + z?…

A: Given: Surface of revolution with the equation x2+y2+z2=e2x To find: Identify a generating curve on…

Q: Determine the projection of the surface – y? = z on the yz-plane? (Hint: a = 0) Circle O No answer…

A: The solution is :

Q: Find the area of the surface generated by revolving the curve, x = /6y – y? ; 2sys 5

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Determine the projection of the surface - y = 3. on the yz-plane? (Hint: x = 0) O Parabola O No…

A: Given:      Surface x23-y2=z       By putting x=0 we get             023-y2=z

Q: Find the area of the region enclosed by the parametric equation x = t³ - 7t y = 6t²

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Q: Find the area of the surface generated by revolving the curve about each given axis. x St, y 2t, 0st…

A: Given that        x = 5t , y = 2t  , 0 &lt;= t &lt;= 5  Here we have to find the area of the surface…

Q: Find the surface area of the object obtained by rotating y = +÷, 1 1<x<2 about the x-axis.

A: To find the surface area of the object obtained by rotating y=x36+12x ,  1≤x≤2 about x-axis.  Let,…

Q: Find the area of the surface that is generated by revolving the portion of the curve y = 2/1-, zE…

A: Use formula of surface area revolved about x axis

Q: HW: Find the area of the surface generaled by revolving 3DVy, 1 <y<8 about the X- axis. 1. 3.

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Which one, y=ex, 1≤y≤2, gives the surface area of the solid formed by rotating the curve segment…

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Q: Find the area of the surface generated by revolving x = t+2/3, y =+2/3t+1, -2/3 sts2/3 about the…

A: Find the area of the surface generated by revolving the graph of the following parametric equation…

Q: Find the surface area generated by rotating the first quadrant portion of the curve  x2=16-8y about…

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Q: Evaluate the exact area of the surface obtained by rotating the circle x2 + y² = r² about the line y…

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Q: Find the area of the region enclosed by the parametric equation x = t3 – 8t y = 6t2

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

A: Note: "Since you have asked multiple questions, we will solve the first question for you. If you…

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: Find the area of the surface of rotation created y = /2x – x2; <a< by rotating this curve around the…

A: By using area of surface formula, we calculate the required area of surface.

Q: Find the area of surface that is generated by revolving the portion of the curve x = V64 – y² , – 2…

A: Solution :-

Q: Determine the projection of the following surface on the xz plane -y+ 름 =1 O Ellipse O Parabola O…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V1+ e*,…

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Q: find the surface area obtained by rotating the circle (x – 4)2 + y? =1 about the y-axis. %3D

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.

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Q: Find the area of the surface obtained by rotating the curve y = 5x° from æ = 0 to æ = 9 about the…

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Q: "ind the area of the surface generated by revolving the curve x = 2/1- y, –1< y <0 bout the y-axis.

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Q: Find the exact area of the surface generated by revolving the curve about the stated axis. y = Vx…

A: The formula for area of surface generated by the revolution of curve y=f(x) , a≤x≤b about x-axis.…

Q: Find the area of the surface obtained by rotating thecircle x2 + y2 = r about the line y =r.

A: We have to find the area of the surface obtained by rotating the circle x2 + y2 = r about the line y…

Q: Use traces to help identify the surface y = 9x2+25z?. O a. Hyperbolic paraboloid b. Cone O c.…

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Q: Find the area of the surface that is generated by revolving the portion of the curve y = x between x…

A: Given; y=x^2 between x=1 to x=2

Q: Find the area of the surface that is generated by revolving the portion of the curve y = x between x…

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Q: Find the area of the surface obtained by rotating the curve y² = 4x + 4 0<x<8 about the x-axis?

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