Find the area of the surface generated when the curve y = √(5x − x2) for 1 ≤ x ≤ 4 is revolved about the x-axis.

Q: Find the surface area if y = (x3/6)+(1/2x) on .5<=x<=1 is rotated about the x-axis.

A: Given: y=x36+12x on 5≤x≤1

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

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Q: For numbers 1-2, consider a plane bounded by the curves y=9-x² and y=x+3. 1. What is the desired…

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

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Q: Identify and sketch the surfaces x2 + y2 + z2 = 4

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Q: 6. Find the area of the surface generated when y = v4x + 6 is revolved about the x- axis on the…

A: 80π

Q: Find, to two decimal places, the areas of the surfaces generated byrevolving the curves about the…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

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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: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x? A. y² + z² =…

A: Given: The equation of surface which is z2-xz=lnx+3x. This equation is a quadratic equation for z.…

Q: Find the area of the surface generated when the curve is revolved about the y-axis. y=4x-1, for 1 <…

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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: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)²=2y, the…

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Q: Find the surface area of the surface when f(x)=x3 on [0,2].  Is rotated about the y-axis and about…

A: Use surface area formula

Q: The surface area of the surface generated by revolving y= 1 – x² for 0<x<1 about the x – axis is s=…

A: The solution is as follows

Q: The area, in square units, bounded by the curves y = x² , y=2 – x and y=1 is ,

A: For a bounded figure, to find the area we need to determine the limits and the curves we need to…

Q: Describe the level surfaces for f (x, y, z) = y+10-√√x² + z² and sketch them for several (at least…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

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Q: Given the expression x⁴-3x+7=y³ on the interval [3,5], determine the surface of revolution if it is…

A: Given that, the expression is x4-3x+7=y3.

Q: 5. Consider the two curves y = x° - 3x + 20x + 88x² + 71x – 74 and y = 2a+ 50x – 22x + 42.x + 31. |…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

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Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y = V3x +5…

A: Surface area of the bounded region along x axis

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

A: We have to calculate the area of the smaller region bounded by x+52=2y from left sides,and bounded…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2=2y, the…

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Q: Sketch the section of the surface at y = 0. 1 + x² + y² Z = 4 -8 -6 -4 -2 4 4 6. 4 -8 -6 -4 -2 2. 4…

A: Given data is: To sketch the surface at y=0 z=1+x2+y2

Q: Find the area of the surface generated when the given curve is revolved about the y-axis. y = (x^2…

A: Solution:

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

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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: 4. Find the area of the surface generated when the given curve is revolved about the y-axis. y=(2x)"…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: find the surface area of the portion of the curve x²+y²=4 from x=0 to x=2 when it is revolved about…

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Q: Suppose that the curve y =( x^4)/8 + 1/(4x^2) on the interval [1, 2] was revolved about the x-axis.…

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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:

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)² = 2y, the…

A: The shaded region is our required area

Q: The surface area of the surface generated by revolving y= 1-x2 for 0<x<1 about the x - axis is S = […

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Q: (a) Find the area of the surface generated by the given curve about x-axis y = V, (b) Find the area…

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Q: The area of the surface obtained by rotating the curve y = √√x + 1, for 0 ≤ x ≤ 2, about the x-axis,…

A: Given :

Q: Find the area of the surface generated when y² = 12x is revolved about the x- axis from x = 0 to x =…

A: Given curve,y2 = 12xRevolved about x-axis from x=0 to x=3.

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 the points on surface z^2=xy+4 closest to origin.

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Q: If 0 ≤ f (x) ≤ g(x) for x in the interval [a, b], can the surface obtained by rotating the graph of…

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Q: Suppose surface #1 is defined by =45°,0<p< 5, 0 <z< 8 and surface #2 is defined by 0=32° The length…

A: The diagram for the surface 1 is, The diagram formed is rectangle.

Q: Find the area of the surface generated when the given curve is revolved about the given axis. y = 12…

A: Consider the curve y=12-3x, 1⩽x⩽3. Surface area of solid when curve is rotated around x-axis is…

Q: Calculate the area of the surface generated when the curve, f(x) = x3/2 – on [1,2 ] is x'/2 revolved…

A: The surface area will be given by S=∫ab2πy1+dydx2dx

Q: 10. Given the expression x* – 3x + 7 = y* on the interval [3,5], determine the surface of revolution…

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

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Q: (#2) Find the area of the surface generated by revolving the curve about x-axis for f(x) = 2Vx on…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. < =v² + 2)3/2, 3…

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