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Q. The first fundamental form of of the surface (S) is given by I(du, dv) = udu + 4vdudv + d'v. Consider the transformation 0 = u – v, 0= u. Then I(d0, do) = 1.(1 – 40 + 5ø) d0 + (40 – 40 – 2)d0do + d°o 2.d0 + (40 3.d? о + (1 -40+ 5ф) dвdф + (40- 4ф— 2)d? ф 4.d0 + (4ø – 460 – 2)dedo + (1- 40 + 5ø) d²o 5. None of these. - 4ф - 2)d0dф + (1 - 40 + 5ф) d ф —

Q. The first fundamental form of of the surface (S) is given by I(du, dv) = udu + 4vdudv + d'v. Consider the transformation 0 = u – v, 0= u. Then I(d0, do) = 1.(1 – 40 + 5ø) d0 + (40 – 40 – 2)d0do + d°o 2.d0 + (40 3.d? о + (1 -40+ 5ф) dвdф + (40- 4ф— 2)d? ф 4.d0 + (4ø – 460 – 2)dedo + (1- 40 + 5ø) d²o 5. None of these. - 4ф - 2)d0dф + (1 - 40 + 5ф) d ф —

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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Q. The first fundamental form of of the surface (S) is given by I(du, dv) = udu + 4vdudv + d'v. Consider the transformation 0 = u – v,o= u. Then I(d0, do) = 1.(1 40 + 5ø) d'0 + (40 – 40 – 2)d0dh + d'o 2.d0 + (40 - 4ø – 2)d0do + (1– 40 + 50) d'o 3.20 + (1 - 40 + 5ø) dodo + (40 – 40 – 2)d²o 4.d0 + (40 – 40 – 2)dedo + (1– 40 + 5ø) d?o 5. None of these. - Option 1 Option 2 Option 3 Option 4 Option 5 Q. If u = u(0, ø), v = v(0, ) transforms the first fundamental form of a surface (S) I(du, du) = ud'u+udv into I(d0, do) = d'0+(0 +)° d¢, where u, v, 0,o> 0,then the Jacobian of the transformation equals 1.J = 2.J = 3.J = 0+の 4.J = 0+の 5. None of these. Option 1 Option 2 Option 3 Option 4 L0 Option 5
Transcribed Image Text:Q. The first fundamental form of of the surface (S) is given by I(du, dv) = udu + 4vdudv + d'v. Consider the transformation 0 = u – v,o= u. Then I(d0, do) = 1.(1 40 + 5ø) d'0 + (40 – 40 – 2)d0dh + d'o 2.d0 + (40 - 4ø – 2)d0do + (1– 40 + 50) d'o 3.20 + (1 - 40 + 5ø) dodo + (40 – 40 – 2)d²o 4.d0 + (40 – 40 – 2)dedo + (1– 40 + 5ø) d?o 5. None of these. - Option 1 Option 2 Option 3 Option 4 Option 5 Q. If u = u(0, ø), v = v(0, ) transforms the first fundamental form of a surface (S) I(du, du) = ud'u+udv into I(d0, do) = d'0+(0 +)° d¢, where u, v, 0,o> 0,then the Jacobian of the transformation equals 1.J = 2.J = 3.J = 0+の 4.J = 0+の 5. None of these. Option 1 Option 2 Option 3 Option 4 L0 Option 5
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