AIS. 4. Compute the area of the surface formed when f(r) = 2 + cosh(r) between 0 and i is rotated around the z-axis. > ph of fír) 1/z, z>1, around the z-axis.
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- 1) Find the area of the surface generated by rotating the function y=x^3 about the x-axis over 0≤x≤3 2) Find the area of the surface generated by rotating the function g(y) = (9-y^2) ^1/2 about the y-axis over 0≤y≤2.Find the point(s) on the surface z2=xy+1 which are closest to the point (4, 2, 0).1. Consider the surface defined by z = x2 + e9y ln(x-y). Let f(x,y) = x2 + e9y ln(x-y). ○ Compute ∇f at the point (1,0). ○ Compute the derivative of f(x,y) at the point (1,0) in the direction (3,-4). ○ Explain the geometric relationship between the answer found in part (a) and the surface defined above.
- Sketch the trace curves of x^2 − y^2 + z^2 − 4x + 2z = 4, and use these trace curves to sketch the surface in R^3Rotate the graph of g(x)=e^(−6x) on the interval [0,8] about the x-axis to generate a surface with area= square units.what is the area of the rotational surface formed by rotating the part of the function y= x^3/3 between 0<x<1 around the Ox axis
- If 0 ≤ f (x) ≤ g(x) for x in the interval [a, b], can the surface obtained by rotating the graph of y = g(x) around the x-axis over the interval have less surface area than the surface obtained by rotating the graph of y = f (x) around the x-axis over the same interval?1- The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 1/3x3/2, 0 ≤ x ≤ 12 2- The given curve is rotated about the y-axis. Find the area of the resulting surface. x = (a2 -y2 )1/2 , 0 ≤ y ≤ a/9 3- If the infinite curve y = e−7x, x ≥ 0, is rotated about the x-axis, find the area of the resulting surface. 4- Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare your answer with the value of the integral produced by a calculator. (Round your answers to six decimal places.) y = 5xex, 0 ≤ x ≤ 1Consider the curve C shown in the attached figure, which is the intersection between the surfaces S1 and S2, with S1: z = 4 - x2 and S2: x + y = 4a, for a > 1. Furthermore, the curve Cit is bounded by the planes z = 0 and z = 3x. A parameterization of curve C is: See the possible answer in the image