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In the following series of questions, we consider Catalan's surface, which is the image of Assume that we define on a sufficiently small open set UC R² so that o is a regular surface patch, and let S be its image. It can be shown (and you can assume) that ou 6 = 0 and What is E? o(u, v) = (u – sin(u) cosh(v), 1 − cos(u) cosh(v), −4 sin( - Select one: O a. 0 in² (1) |ou|² = |o₂|² = 4 (sin² (¹) sinh ¹(²)). + cosh² ( ² ) − 1) O b. 2√/sin²(u/2) + cosh²(v/2) - 1 cosh(v/2) O c. 4√√/sin²(u/2) + cosh²(v/2) — 1 cosh(v/2) ○ d. 4 (sin²(u/2) + cosh²(v/2) − 1) cosh²(v/2) ○ e. 8 (sin² (u/2) + cosh²(v/2) - 1) cosh² (v/2) O f. (1 - cos u cosh u, sin u cosh v, -2 cos(u/2) sinh(v/2)) O g. (– sin u sinh v, – cos u sinh v, −2 sin(u/2) cosh(u/2)) O h Not determined from the given information. The Riemannian metric of o can then be written, in standard notation, in terms of the coordinates u, v as g= Edu² + 2F du dv + G dv². ²(²). cosh²

In the following series of questions, we consider Catalan's surface, which is the image of Assume that we define on a sufficiently small open set UC R² so that o is a regular surface patch, and let S be its image. It can be shown (and you can assume) that ou 6 = 0 and What is E? o(u, v) = (u – sin(u) cosh(v), 1 − cos(u) cosh(v), −4 sin( - Select one: O a. 0 in² (1) |ou|² = |o₂|² = 4 (sin² (¹) sinh ¹(²)). + cosh² ( ² ) − 1) O b. 2√/sin²(u/2) + cosh²(v/2) - 1 cosh(v/2) O c. 4√√/sin²(u/2) + cosh²(v/2) — 1 cosh(v/2) ○ d. 4 (sin²(u/2) + cosh²(v/2) − 1) cosh²(v/2) ○ e. 8 (sin² (u/2) + cosh²(v/2) - 1) cosh² (v/2) O f. (1 - cos u cosh u, sin u cosh v, -2 cos(u/2) sinh(v/2)) O g. (– sin u sinh v, – cos u sinh v, −2 sin(u/2) cosh(u/2)) O h Not determined from the given information. The Riemannian metric of o can then be written, in standard notation, in terms of the coordinates u, v as g= Edu² + 2F du dv + G dv². ²(²). cosh²

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In the following series of questions, we consider Catalan's surface, which is the image of ¹(²)). Assume that we define o on a sufficiently small open set UC R² so that o is a regular surface patch, and let S be its image. It can be shown (and you can assume) that ov = 0 and What is E? И o(u, v) = u - sin(u) cosh(v), 1 - cos(u) cosh(v), -4 sin 2 ¹² (1) + cosh² ( ² ) − 1) cosh² (-). The Riemannian metric of a can then be written, in standard notation, in terms of the coordinates u, v as g = Edu² + 2F du du + G dv². Select one: O a. 0 O e. |ou|² = |ov|² = 4 (sin² O b. 2√/sin² (u/2) + cosh²(v/2) - cosh(v/2) O c. 4√/sin² (u/2) + cosh² (v/2) - 1 cosh(v/2) ○ d. 4 (sin²(u/2) + cosh²(v/2) − 1) cosh²(v/2) 8 (sin²(u/2) + cosh²(u/2) – 1) cosh²(v/2) sinh O f. (1 - cos u cosh v, sin u cosh v, -2 cos(u/2) sinh(v/2)) g. (− sin u sinh v, – cos u sinh v, −2 sin(u/2) cosh(u/2)) Oh. Not determined from the given information.
Transcribed Image Text:In the following series of questions, we consider Catalan's surface, which is the image of ¹(²)). Assume that we define o on a sufficiently small open set UC R² so that o is a regular surface patch, and let S be its image. It can be shown (and you can assume) that ov = 0 and What is E? И o(u, v) = u - sin(u) cosh(v), 1 - cos(u) cosh(v), -4 sin 2 ¹² (1) + cosh² ( ² ) − 1) cosh² (-). The Riemannian metric of a can then be written, in standard notation, in terms of the coordinates u, v as g = Edu² + 2F du du + G dv². Select one: O a. 0 O e. |ou|² = |ov|² = 4 (sin² O b. 2√/sin² (u/2) + cosh²(v/2) - cosh(v/2) O c. 4√/sin² (u/2) + cosh² (v/2) - 1 cosh(v/2) ○ d. 4 (sin²(u/2) + cosh²(v/2) − 1) cosh²(v/2) 8 (sin²(u/2) + cosh²(u/2) – 1) cosh²(v/2) sinh O f. (1 - cos u cosh v, sin u cosh v, -2 cos(u/2) sinh(v/2)) g. (− sin u sinh v, – cos u sinh v, −2 sin(u/2) cosh(u/2)) Oh. Not determined from the given information.
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