1. (20 marks) (a) (4 marks) Derive a formula for the surface area of an object that is created by rotating a function f(x) around: 1. the r-axis with y20 2. the y-axis with 20 You will need to clearl...

Question

Question

1. (20 marks) (a) (4 marks) Derive a formula for the surface area of an object that is created by rotating a function f(x) ar

math algebra

Answer 1

Answer #1

Answer 2

Similar Homework Help Questions

2. (20 marks) (a) Calculate the surface area of the graph of f(x,y) = x +...

2. (20 marks) (a) Calculate the surface area of the graph of f(x,y) = x + 20y over the region R= {(x,y) e R2:1 < x < 4,2 sy s 2x} in the xy-plane. OV (b) Integrate the function g(x, y, z) = x +y +z over the surface that is described as follows: x = 2u – v, y = v + 2u, z= v – u Here u € [0,20), v € [0,21].
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (...

Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (i Determine the level curves for the surface when z on the same diagram in the r-y plane. 1 and 2, Sketch the level curves (i) Determine the cross-sectional curves of the surface in the r-z plane and in the y- plane. Sketch the two cross-sectional curves (iii) Sketch the surface. (b) For the point (r, y)...
(2) The area of the surface with equation z = f(x,y). (x,y) E D. where fra...

(2) The area of the surface with equation z = f(x,y). (x,y) E D. where fra f, are continuous, is A(S) = SVGC3. y)]? + [f;(x, y)]? +T dA If you attempt to use Formula 2 to find the area of the top half of the sphere x + y2 + 2? = a, you have a slight problem because the double integral is improper. In fact, the integrand has an infinite discontinuity at every point of the boundary circle...

only number 5-7. Just set up no solve. show all work 1) Rotate the area bound by f(x): 2x + 1, y : O, x-1, and x : 4 around the x- 2) Rotate the area bound by y : x2 , y :0, and x-2 around the y-axis....

only number 5-7. Just set up no solve. show all work 1) Rotate the area bound by f(x): 2x + 1, y : O, x-1, and x : 4 around the x- 2) Rotate the area bound by y : x2 , y :0, and x-2 around the y-axis. #3-7: Draw a graph and setup the integral, including boundaries for determin the solid created. You do NOT need to evaluate the integrals. 3) Rotate the area bound byy and ya...
4. Define the function f: 0,00) +R by the formula f(x) = dt. +1 Comment: The...

4. Define the function f: 0,00) +R by the formula f(x) = dt. +1 Comment: The integrand does not have a closed form anti-derivative, so do not try to answer the following questions by computing an anti-derivative. Use some properties that we learned. (a) (4 points). Prove that f(x) > 0 for all x > 0, hence f: (0,00) + (0,0). (b) (4 points). Prove that f is injective. (c) (6 points). Prove that f: (0,00) (0,00) is not surjective,...