Answered: Consider the region, R, bounded by the…

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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Find the equation of the tangent plane to the graph of f(x, y) = 8x² – 2xy? at the point (5, 4). A) z = 23x – 15y + 42 B) z = 48x – 80y + 120 C) 0 = 48x – 80y + 120 D) 0 = 23x - 15y + 42
- Let F= (y-r, r+y) and C be the closed, piece-wise smooth curve in the zy-plane consisting of: C : the directed line segment from (a, 0) (a, a), followed by C2: the directed line segment from (a, a) (0, a), followed by; C3: the path along the quarter circle + y = a? from (0, a) -→ (a, 0). a) For what values of a > 0 is f, F. dr = 0? b) Is the line integral f. F. dr path-independent on R?? Explain.
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Consider the region, R, bounded by the piecewise smooth curve, C, that goes from (0,0) to (2,0) to (0,2) back to (0,0). Let 2 F=2x i+3y j. 2 (i) Compute the line integral of F on the boundary of R directly. (ii) Compute this using Green's Theorem.