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(d) The lines 1(1) = (1 – t, 1 + 1, 21) and I2(t) = (4 – 21,3 + 21, 1 + 5t) are parallel. True False

(d) The lines 1(1) = (1 – t, 1 + 1, 21) and I2(t) = (4 – 21,3 + 21, 1 + 5t) are parallel. True False

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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(d) The lines /1(t) = (1 – t, 1 + t, 2t) and l2(t) = (4 – 2t, 3 + 2t, 1 + 5t) are parallel. True False (e) Let f : R² → R be a function where all second order partial derivatives exist and are not continuous for all points (x, y) E R². Then дудх -(x, y) = āxây ,(x, y) for all points (x, y) E R². True False (f) Let f : R² (x, y) E R². Then → R be a function where all second order partial derivatives exist and are continuous for all points : (х, у) — arar (x, y) for all points (x, y) E R². дхду дудх True False (g) Let f(x, y) be a C² function which has a local maximum at (0, 0). Then the Hessian matrix of f at (0,0) is necessarily negative definite. True False
Transcribed Image Text:(d) The lines /1(t) = (1 – t, 1 + t, 2t) and l2(t) = (4 – 2t, 3 + 2t, 1 + 5t) are parallel. True False (e) Let f : R² → R be a function where all second order partial derivatives exist and are not continuous for all points (x, y) E R². Then дудх -(x, y) = āxây ,(x, y) for all points (x, y) E R². True False (f) Let f : R² (x, y) E R². Then → R be a function where all second order partial derivatives exist and are continuous for all points : (х, у) — arar (x, y) for all points (x, y) E R². дхду дудх True False (g) Let f(x, y) be a C² function which has a local maximum at (0, 0). Then the Hessian matrix of f at (0,0) is necessarily negative definite. True False
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