What are the reace curves of this surface for x=0, y=0, and for z=k? Name the shape of the surface. x2-y2=z

Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x2 , (z =…

A: The distance of any points ( having same y co-ordinate ) on the curve is at same distance from…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 2 + 2)3/2, 1s ys…

A: The curve x=13y2+232 revolved about x-axis on 1≤y≤4

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y= x3/6 + 1/2x ,…

A: Given that the curve is

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x3 y = 2 1 6x' 2

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Q: Find an equation for the surface obtained by rotating the line z = 7y about the z-axis.

A: We need to determine the equation of the surface that is obtained by rotating the line z=7y about…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. =x²+²x≤x≤1 3x 2…

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Q: The area of the surface obtained by rotating the curve y = x2, 0 <x< 12 about the y-axis is

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x -(y2 + 2)3/2,…

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Q: The area of the surface obtained by rotating the curve y = x2, 0sxs1 about the y-axis is

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Q: Find the surface area of the portion of the sphere generated by revolving the curve y = 1- x², 0sis…

A: y=1-x2,  0≤x≤12 Differentiating with respect to x, we get dydx=121-x2·0-2x=-x1-x2

Q: Find the exact area of the surface obtained by rotatingthe curve about the x-axis. y = x3 ,  0 ≤ x ≤…

A: Given  y =x3 ,  0 ≤ x ≤2The area under a curve is the area between a curve f(x)and the x-axis on an…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.   y = 5− x, 3 ≤…

A: To find the exact area of the surface obtained by rotating the curve about the x-axis.  y = 5− x, 3…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V8 - x, 25…

A: given, y=8-x  ,2≤x≤8  the graph is

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y=x3,…

A: If the curve y = f(x), a ≤ x ≤ b is revolved about the x-axis, then the area of the resulting…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 y = + /- 2x

A: Given: The equation of the curve y=x36+12x,where  12≤x≤1. Calculation: Compute the surface area as…

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

A: Given:  y = (x3)/(6)+(1)/(2x),   1/2 ≤ x ≤ 1

Q: Find the area of the surface obtained by rotating the curve x = /16 – y², 0 <y<2, about the y- axis.…

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

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x3, 0 < x <…

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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: Given a surface, ƒ(x,y,z)=15, explain what you would do to find the equation of the tangent plane at…

A: Nothing

Q: Find the exact area of the surface obtained by rotating the curve about the  x-axis.   x = 1/3 ( y2…

A: Given curve is x=13y2+232 over 1 ≤ y ≤ 2. The exact area of the surface obtained by rotating the…

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

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V6 - x, 4 <…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y =(5-x)^1/2…

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Q: Suppose that an equation for the surface is S(x,y) = xye^x. In what direction (relative to the…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. X = 2 + 3y2, 1 <…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √7-x, 1 ≤x≤7

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x³, 0 < x <…

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Q: Find the exact area of the surface obtained by rotating the curve about the y- axis: y = 3 + 5x?,…

A: Consider the given function and interval. y=3+5x2, 3≤x≤8 If y=f(x) is function and the interval of y…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.  x=1+5y2,…

A: Recall: Area of the surface rotating about the x-axis: If the curve x=g(y) is given , c≤y≤d , and…

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

A: Given the equation4x2+9z2=36

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x3,    0 ≤…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x³, osx S 5

A: Given data:   The given equation is y=x3. The given limits of x are [a,b]=[0,5].   Differentiate the…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x³, 0 < x< 5

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1/3(y2 +…

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Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x.(z 0)

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1/3(y2 +…

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Q: Let C be the curve y =x3/2, 1 < x < 4. (a) Find the length of this curve. (b) Find the surface area…

A: Given curve is

Q: Find the exact area of the surface obtained by rotating the curve about the  x-axis.   x = 1+ 2y2 ,1…

A: Find the exact area of the surface obtained by rotating the curve about the  x-axis.   x = 1+ 2y2 ,1…

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

A:

Q: Find the exact area of the surface obtained by rotatingthe curve about the x-axis. y =√(1+ 4x)  ,  1…

A: Find the exact area of the surface obtained by rotatingthe curve about the x-axis.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 5 + 4y2,…

A: We use the formula S=2π integration of y √(1+x'2)dy from 1 to 2

Q: Find an equation for the surface of revolution formed by revolving the curve z2 = 2y in the yz-plane…

A: To find the equation for the surface of revolution

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: メ y= oL Xとn2

A: Given curve is y=ex , 0≤x≤ln2find the area of the surface

Q: Find the area of the surface obtained by rotating the curve y=1/3 x3/2, 0≤y≤12  about the y- axis.

A: Let a rectangular strip parallel to x-axis of thickness dy be made whose tip touches the curve…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V8 - x, 2 s…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.  x=1/3(y2 + 2)…

A: The given curve is,

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.…

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.