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

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: The slope of the surface z = xy² in the x-direction at the point (2, 3) is _____, and the slope of…

A: Given:z=xy2   x-directionat the point 2, 3 y-directionat the point 2,3

Q: of the tangent plane to the surface z=e-4x/17ln(1y) at the point (-3, 4, 2.808).

A:

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

A: 80π

Q: 5. Use traces to sketch and identify the surface x2- y? - z2 = 4.

A:

Q: The area of the surface formed by revolving the graph of x = /ỹ on [2,9] about the x-axis is given…

A:

Q: what is the area of the rotational surface formed by rotating the part of the function y= x^3/3…

A: We apply the above formula to solve this

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: 1. Find the area of the surface z = k + xy inside the cylinder x² + y² = R² for constant R. k > 0 is…

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: [39] Consider the heat conduction in a circular cylinder: x² + y² < a²,0 < z <b. Assume that the…

A: Given Data: Heat conduction in a circular cylinder  x2+y2&lt;a2, 0 &lt;z&lt;b To Find: (a) Boundary…

Q: find Ix, Iy, I0, x, and y for the lamina bounded by the graphs of the equations. y = 0, y = 2, x =…

A: The value of I0,Ix,Iy.

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: A surface has Cartesian equation :- f(xy). given by f(1.9)=6xy-5x -3y+ +7x-6y a) Use any…

A: To graph the function: z=f(x,y) where f(x,y)=6xy-5x2-3y4+7x-6y

Q: Find an equation for the plane that is tangent to the given surface at the given point. z= vy-x…

A: Here, the given surface is: z=y-x Now, ∂z∂x=12y-x(-1)=-12y-x∂z∂y=12y-x(1)=12y-x Now, at (0,4,2):…

Q: over the open surface S given by the upper part (only) of the intersection of ti of the function z =…

A: Introduction: Stokes Theorem (also known as Generalized Stokes Theorem) is a statement about the…

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

A: Given : Curve y= √(5x − x2)  For 1 ≤ x ≤ 4 is revolved about the x-axis.

Q: Find the absolute maximum and minimum values of f(x, y) = 3xy−6x−3y + 7 on the closed triangular…

A: Find out the absolute maximum and minimum values of  f(x,y)=3xy-6x-3y+7 for the maximum and minimum…

Q: Given a surface f(x,y) = -2x² + (-3)y“. Find the derivative in the direction of v = at the point…

A:

Q: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

A:

Q: Given the curve x = 2 y – y´ and the line x = 0 Find the ordinate of the centroid y of the region…

A:

Q: Find the absolute maximum value of the function f(x, y) = 3x² + 2y² – 4y+1 | on the disk which has…

A:

Q: Find the absolute maximum and minimum of f(x,y)= 4xy^2 - (x^2)(y^2) - xy^3 on the closed triangular…

A: f(x,y)=4xy2-x2y2-xy3fx=4y2-2xy2-y3fx=04y2-2xy2-y3=04-2x-y=0…

Q: Given a surface f(x,y) = -3x² + (-4)y“. Find the derivative in the direction of v = at the point…

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: Given a surface f(x,y) = -2x² + (5)y². Find the derivative in the direction of v = at the point (7,…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y=(x3/3+1/(4x))…

A: The given curve is: y=x33+14x ;            12≤x≤1

Q: i) The area of the surface obtained by the rotating the curve y=V 16-x², -1s×<1 about the x-axis is

A: As per the company's guidelines, we are supposed to solve first question for you,  kindly repost the…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y =  x3 4 +  1…

A: Sarface area problem....

Q: 1_2 Can you please help me with this example in a step by step guide. Thank you very much!!

A: To calculate the coordinates (x,y,z) and also define the absolute extremum for the provided surface…

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: 2. Find an equation for the plane tangent to the surface 3x2 - 4xy+ z2 = 0 at the point (1, 1, 1).…

A:

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 the surface revolved for the x-axis is, z2-xz=ln(x)+3x

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

A:

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: 3. Find the extreme values of the given f(x, y) on the indicated surface. f (x, y) = 8x² – 2y; x² +…

A: The solution of the problem is given in the next step.

Q: Determine the area of the surface of revolution defines by the function f(x) = V1 - x,0 <xS; 2.…

A:

Q: Find the surfaces on which the function u = 2 (x2 + y²)/z is constar

A: Since u is a constant so, x2+y2z=4a , where a is an arbitrary constant.

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

A: This is a problem related to find area of the curve using integration. Please use below method to…

Q: Q3. Find the point(s) on the surface xyz 1 closest to the origin. %3D

A: Given: To find the points on the surface xyz=1 is given as,

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: 4. Find the area enclosed by: a. y= sin(x) and y cos(x), x=0, x = and the y-axis. b. y=x and y =Vx.…

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: 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: of the solid in revolution as it axis and the function 2 – x) 0<x< 2

A: The given function is fx=x2-x,    0≤x≤2. Find the volume of the solid in revolution as it rotates…

Q: (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 - x², y = 0, and y = 4

A: Consider the given function fx,y,z=x-y.  The region E is enclosed by the surfaces…

Q: An open rectangle box with volume 2m2 has a square base .express the surface s of the box as a…

A: Please find hand written solution.

Q: The volume of the solid generated by the curve y = e¬ª, between x = 3 and x = 7 about the |3| x –…

A: