14. The surfaces p = 1 +sin m0 sin nø have been used as models for tumors. The "bumpy sphere" with m = 5 and n = 5 is shown in the Figure. Find the volume or approximate volume of the tumor.

Q: 8. If A-a- cos0)à, - phå, +zcos*¢â, what is 9. For the conical surface 0= 30",0SOS 27,0Sr52, the…

A: 8. Consider the given vector, A=ρ41-cosϕa^ρ-ρϕa^ϕ+zcos2ϕa^z The formula for divergence in spherical…

Q: (7) Let D be the solid above the cone z = r and below the sphere of radius 2, and let fla, 4, 7) =…

A: To convert the cartesian coordinates into cylindrical coordinates put  And the integral will be…

Q: 4: Show yor work. a) 1: Find the exact area of the surface obtained by rotating the curve y? +x =5,…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Identify and sketch the graph of the following SURFACES. x² + y² = sin² z, Z = [0, π]

A: Given.   x^2+y^2=sin^2z

Q: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

A:

Q: 28. F(x, y, z) = x³i+y°j+z°k, and S is the sphere of radius 3 and centered at the origin.

A: divF→=ddxx3+ddyy3+ddzz3        =3x2+3y2+3z2        =3x2+y2+z2  by divergence theorem,…

Q: 9.3.16. Compute the surface area of the surface obtained by revolving the given curve about the…

A: (a) To compute the surface area of the surface obtained by revolving the given curve about the…

Q: Suppose the temperature at the point (x, y, z) on the sphere x2 + y2 + ?2 = 16 is T= 800xy2z3 .…

A: Solution is given below:

Q: Sketch the surfaces CYLINDERS z = y2 - 1

A: We need to sketch the surface formed by the function

Q: 1 Find the area of the surface obtained by rotating the curve y = In(1 – x²), 0 < x <. about the

A:

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

A:

Q: 16 The area under the curve 4y? (x2 + 1)3 was rotated about a line located to the left 9 of y – axis…

A:

Q: 2-By revolving the semicircle: X= r cos t, Y=r sin t, (0<t<n) About the x-axis, Show that the…

A:

Q: 3) Find the area of the surface obtained by rotating the given curve about the indicated line, y=x2,…

A:

Q: If the infinite curve y = e-6x, x > 0, is rotated about the x-axis, find the area of the resulting…

A:

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

A:

Q: 18. Find the surface area of the sphere with radlus 5 by dou- bling the surface area of (x, y)…

A: Given: f(x,y)=25-x2-y2 is the surface bounded by the circle x2+y2=25 where radius, r=5

Q: For the solid region W described and shown in Problem 3, write the limits for fw f dV in the…

A:

Q: 3. Find the area of the surface generated by revolving the curve y = 2/x ,1Sx<2, about the x-axis(as…

A:

Q: Find the surface arca of y = (1/3)r 10<x <1 revolved about the z-ax

A: Given: The equation is y = 13x3 , 0 ≤x≤1 revolved about the x - axis.

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 +y? + 2? = 1 is T =…

A:

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

A:

Q: 2. The portion of a cylinder of radius 3 centered along the y-axis that lies between the planes y =…

A:

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: 4. If the curve y = 3 – x², 0<x<4 is rotated about the y-axis, find the area of the resulting…

A:

Q: 4. Find the area of the surface obtained by rotating the curve y? = x + 1, 0<x < 3. about the x-axis…

A:

Q: ded above by surface z = 10 – x2, bou e planes y = 0 and y = 3.

A:

Q: Find the points on the surface y2 = 4 + xz that are closest to the origin. (Enter your answers from…

A: Consider the given surface equation y2=4+xz.  The distance d between the origin 0,0,0 and any point…

Q: 1 Find the surface area of the part of the hyperbolic paraboloid z = (x² - y²) that lies inside the…

A:

Q: What is the equation of the plane to the surface z = e3Y sin(3x) +2 at the point P,0, 3) O x- y + ez…

A:

Q: 5. Find the exact area of the surface generated by revolving the given curve about the y- axis, Draw…

A: Application of integration

Q: Determine the surface of revolution if the arc y^3 + y = x^2 + 6x on the interval [−5, −1] is…

A: The curve will appear like this

Q: 3. Find the exact area of the surface resulting from rotating y = v1 + e* from x = 0 to x = 1 about…

A:

Q: 4: Show yor work. a) | 1: Find the exact area of the surface obtained by rotating the curve y? +x…

A:

Q: 1. Find the area of the surface generated by revolving the given curve about the x-a (a) y = 7x,…

A:

Q: 9. Using Stoke's Theorem Evaluate [(2x – y)dx – yz dy – y zdz) where c is the circle x +y =1,…

A:

Q: y = cos(x), 0 <x<

A: Consider the given surface whose area is required to calculate.

Q: 8) Find the area of the surface generated by rotating about the x-axis the arc of the curve y x…

A:

Q: If the infinite curve y = eSX, x > 0, is rotated about the x-axis, find the area of the resulting…

A:

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

A:

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

A: The area of the surface obtained by rotating the curve about x-axis is given by the formula…

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

A:

Q: 6. Find the area and centroidal distances of the curve that lies between the equations y-4-x^2 and…

A:

Q: 13. Find the area of the surface generated when the curve = , on [2,4] is rotated about the y-axis.

A: The solution are next step is

Q: 4) The area of the surface generated by revolving x=y²-1, 1≤ y≤ 2 about x-axis is S=.

A:

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: 10. Find the surface area of the solid generated by revolving the line segment y = vx + 1 , 1 < x <…

A:

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

A:

Q: 15) Consider curve C which is the intersection of the surfaces shown in the attached figure. The…

A: The equation of the graphs given are as follows: x=-34y2+3y=yz=y22 We are asked to evaluate the…

Q: Q#4 a. Find the area of the surface generated by revolving abuut the x – uxis the portion of the…

A: