Question: Let (B) be a smooth surface. Set E = ||u||, F = u and G = ||u||. Prove that the surface area of S is

Let ψ(B) be a smooth surface. Set E = ||ψu||, F = ψu and G = ||ψu||. Prove that the surface area of S is ∫B √E2G2 - F2d(u, v).

Step by Step Solution

★★★★★

3.35 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let x y z u v The... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

741-M-N-A-D-I (769).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Q:

Let C be a smooth C2 arc with parametrization (ɸ, [a, b]), and suppose that s = ï¬(t) is given by (2). The natural parametrization of C is the pair (v, [0, L]), where v(s) =...

Q:

Let S be an orientable surface with unit normal n and nonempty boundary ÏS which satisfies the hypotheses of Stokes's Theorem. a) Suppose that F: S R3{0} is Cl, that ÏS is smooth, and that...

Q:

Let the piecewise smooth, simple closed curve C be the boundary of a region S in the xy-plane. Modify the argument in Example 2 to show that (-y) dx A(S)

Q:

8. Let 'ljJ(B) be a smooth surface. Set E = II'ljJull, F = 'ljJu . 'ljJv, and G = II'ljJvll. Prove that the surface area of 8 is IE vE2G2 - F2 d(u,v).

Q:

1. Let A = {1, 2, 3, 4, 5), B = {0, 1, 4, 8}, and C = {2, 5, 7, 9, 1 1, 13, 17). Compute each of the following (a) AUB. (b) AnB. (c) AnC. (d) A - B. (e) A - (BUC). (f) (A - B) U (A - C). (g) An...

Q:

A discrete sequence {xn} can be converted into a continuous representation x(t) = ts X n= (t n ts) xn, where ts is the sampling period. (a) State two characteristic properties of Dirac's function. [2...

Q:

MAT348-Homework # 3 (20 points, due on Wednesday March 23) Question 1. Let S1 ((Z 26 )10 , (Z 26 )10 , (Z 26 )* , e (1) , d (1) ) be the multiplicative cipher defined by e(1) ( x0 ,, x9 ) (k1 x0 mod...

Q:

Discrete Math Directed Graphs Let us first give the formal definition: Definition (Directed graph). A directed graph is given by a set of vertices V and a transition relation T C V x V. We write 9 =...

Q:

1. The surface S is obtained by rotating the curve y(u) = (cosh u, 0, u) around the z-axis in R. (a) Find a smooth parametrization o(u, v) of S. (b) Show that your parametrized surface o(u, v) in...

Q:

My Scrabble: a game of words This project will take you to your childhood where we loved word games like Scrabble. This game that you are going to code is a lot like Scrabble. Letters are dealt to...

Q:

Draw the β-pyranose form of (a) in its lowest energy chair conformation, and a Fischer projection for (b). (a) (b) CHO CH20H HO OH OH OH Ho Ho OH

Q:

The water depth, D, in metres, in a boating marina on a particular day can be modelled by the function D(t) = 4 sin (30" x t) + 12.5, 0St

Q:

Required Return If the risk - free rate is 1 1 . 2 percent and the market risk premium is 6 . 4 percent, what is the required return for the market? Multiple Choice 1 7 . 6 % 6 . 4 % 1 1 . 2 % 4 . 8 %

Q:

Explain why the following statement is true: = M.

Q:

In a clinical study, volunteers are tested for a gene that has been found to increase the risk for a disease. The probability that a person carries the gene is 0.1. (a) What is the probability 4 or...

Q:

Assume that each of your calls to a popular radio station has a probability of 0.02 of connecting, that is, of not obtaining a busy signal. Assume that your calls are independent. (a) What is the...

Q:

In Exercise 3-70, recall that a particularly long traffic light on your morning commute is green 20% of the time that you approach it. Assume that each morning represents an independent trial. (a)...

Q:

A client has come to you inquiring about establishing a contingency fund for emergency purposes. She tells you that safety of principal is very important but so, too, is the possibility of a higher...

Q:

Maynard's Tools needs a computerized machine tool lathe which costs $95,866 and requires $12,608 in maintenance expense for each year of its 5-year life. After five years, this machine will be...

Q:

nstructions: In a new Word document, complete the following: Linux is an open source variation of the Unix OS and there are many versions of the OS freely distributed on the internet. Research 3...