For each of the following, decide if the given vector field is a gradient of a function f. If so, give find the function f and enter it as your answer; if not, enter the word none for your answer and be sure that you are able to explain why this is the case. (a) [2y) i + [32] j f = (b) [6æ cos(a? + y?)]7 + (6y cos(x? + y?)3: f = (c) [2ay) i+ [a°] j: f = (d) [6x cos(y?)] i + [6y cos(x?)] j: f =
For each of the following, decide if the given vector field is a gradient of a function f. If so, give find the function f and enter it as your answer; if not, enter the word none for your answer and be sure that you are able to explain why this is the case. (a) [2y) i + [32] j f = (b) [6æ cos(a? + y?)]7 + (6y cos(x? + y?)3: f = (c) [2ay) i+ [a°] j: f = (d) [6x cos(y?)] i + [6y cos(x?)] j: f =
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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![For each of the following, decide if the given vector field is a gradient of a function f. If so, give find the function f and enter it as your answer; if not, enter
the word none for your answer and be sure that you are able to explain why this is the case.
(a) [2y) i+ (3z] j: f =
(b) [6x cos(x? + y?)] i + [6y cos(x? + y?)] 3: f =
(c) [2xy] i + [a°]j: f =
(d) [6z cos(y?)]7 + [6y cos(a²)] j: f =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7845e31-eea3-486b-bebd-9e0d054a690c%2F11641db0-11aa-4716-80dc-103b166fbaa1%2Fx808f26_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For each of the following, decide if the given vector field is a gradient of a function f. If so, give find the function f and enter it as your answer; if not, enter
the word none for your answer and be sure that you are able to explain why this is the case.
(a) [2y) i+ (3z] j: f =
(b) [6x cos(x? + y?)] i + [6y cos(x? + y?)] 3: f =
(c) [2xy] i + [a°]j: f =
(d) [6z cos(y?)]7 + [6y cos(a²)] j: f =
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