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2. Let C be the path given by a smooth vector valued function r(t) = S(0)i + g(t)j + h(t)k, astsb be a where a, b are non-negative constants. Let k(x, y, 2) be a continuous scalar funetion defined over R. Use this information to answer the following questions. a) Consider the path C :r(1) = r(21), SIs is it always the case that Justify your answer. b) Consider the path Ca i ni(t) = r("), Vasis vo, is it always the case that K(r, M. =) ds = k(1, W. =) ds? Justify your answer.

2. Let C be the path given by a smooth vector valued function r(t) = S(0)i + g(t)j + h(t)k, astsb be a where a, b are non-negative constants. Let k(x, y, 2) be a continuous scalar funetion defined over R. Use this information to answer the following questions. a) Consider the path C :r(1) = r(21), SIs is it always the case that Justify your answer. b) Consider the path Ca i ni(t) = r("), Vasis vo, is it always the case that K(r, M. =) ds = k(1, W. =) ds? Justify your answer.

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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Please help with question 2b) thanks
10:25 E A D • O * * 19%. 2. Let C be the path given by a smooth vector valued function r(t) = f(()i + g(t)j + h(t)k, a <tsb be a where a, b are non-negative constants. Let k(x, y, 2) be a continuous scalar function defined over R. Use this information to answer the following questions. a) Consider the path C : r,() = r(21), sts is it always the case that r, y, z) ds= k(x, y, 2) ds? Justify your answer. b) Consider the path C2 : r:(t) = r(t*), vāsts vo, is it always the case that Justify your answer. II
Transcribed Image Text:10:25 E A D • O * * 19%. 2. Let C be the path given by a smooth vector valued function r(t) = f(()i + g(t)j + h(t)k, a <tsb be a where a, b are non-negative constants. Let k(x, y, 2) be a continuous scalar function defined over R. Use this information to answer the following questions. a) Consider the path C : r,() = r(21), sts is it always the case that r, y, z) ds= k(x, y, 2) ds? Justify your answer. b) Consider the path C2 : r:(t) = r(t*), vāsts vo, is it always the case that Justify your answer. II
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