Use Ring Method Rotate the region bounded by y = x2 – 2x + 4 and y = x + 14 about the x – axis.

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

A: 80π

Q: Use LaGrange multipliers to find the points on the surface 2² = x² + y² which are closest to (4, 2,…

A: Given surface z2=x2+y2 and the point (4,2,0). The objective is to find the points on the surface…

Q: 2sin2y=2cosy

A:

Q: Use Lagrange multipliers to find the points on the sphere ² + x² + y² − 2y − 10 = 0 closest to and…

A:

Q: Find the centroid of the region cut from the first quadrant by the circle x2 + y2 = a2.

A:

Q: Find the centroid of the triangular region cut from the first quadrant by the line x + y = 3.

A: We will find the x and y-intercept of the triangle.  To find x-intercept we plug y=0 and find x…

Q: Use Lagrange multipliers to find the point whose coordinates are all positive at which the function…

A: To find - Use Lagrange multipliers to find the point whose coordinates are all positive at which the…

Q: Suppose that x and y are two positive real numbers so that x + y = 10. Maximize the product xy

A: To find the solution of the given problem use the second derivative test. Second derivative test:…

Q: use the lagrange multiplier to find extreme points of f(x,y,z) = 2x+z over the intersection of…

A:

Q: y = -a(x – h)? +k (-2.1 , 2.9) (1,n)

A: The given curve is y=-ax-h2+k. Here h=-1 and k=11 given. So the curves becomes y=-ax+12+11. Also the…

Q: Write down the type of this expression, its surfaces, and plot the region bounded by these surfaces…

A: The equations of two intersecting surfaces are provided as: z2=x2+y2 and x2+y2+z2=2. We need to…

Q: linearise R = AT + BT

A: To linearise the below equation. R=AT+BT2

Q: Find div and curl if (x, y, z) = 8y"z' – 10°z° – 3ay div curl

A: Since there is no vector in the given function implies,

Q: Find div F and curl F if F(x, y, z) = xzºi + 6y²x²j + 6z²yk. div F= curl F=

A: