56. Let E(x, y, z) = tan-'(xy + 2z) + zex²-y² + z and let r(t) = (h(t), et²-2t, t²-3t+3) be a parametrization of a curve in space where h(t) is a differentiable function where h(2) = -1 and h'(2) = 4. (a) Find the value of the constant a such that the rate of change of E at the point (x, y, z) = (2,2, -1) in the direction of (x,-1,2) is 18/5. (b) Let ß represent the rate of change of E with respect to t along the path r(t) at t = 2. Find the value of the constant B.
56. Let E(x, y, z) = tan-'(xy + 2z) + zex²-y² + z and let r(t) = (h(t), et²-2t, t²-3t+3) be a parametrization of a curve in space where h(t) is a differentiable function where h(2) = -1 and h'(2) = 4. (a) Find the value of the constant a such that the rate of change of E at the point (x, y, z) = (2,2, -1) in the direction of (x,-1,2) is 18/5. (b) Let ß represent the rate of change of E with respect to t along the path r(t) at t = 2. Find the value of the constant B.
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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Question
![56. Let E(x, y, z) = tan(xy + 2z) + zex²-y²
+z and let r(t) = (h(t), et²-2t, t²-3t+3) be a parametrization of a curve in space where h(t) is a
differentiable function where h(2) = -1 and h'(2) = 4.
(a) Find the value of the constant x such that the rate of change of E at the point (x, y, z) = (2,2, -1) in the direction of (x,-1,2) is 18/5.
(b) Let ß represent the rate of change of E with respect to t along the path r(t) at t = 2. Find the value of the constant ß.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56fd331c-72db-42cb-81f5-18444cd800c1%2Fae51ece6-f976-41cf-9156-f01169569390%2F82b1pg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:56. Let E(x, y, z) = tan(xy + 2z) + zex²-y²
+z and let r(t) = (h(t), et²-2t, t²-3t+3) be a parametrization of a curve in space where h(t) is a
differentiable function where h(2) = -1 and h'(2) = 4.
(a) Find the value of the constant x such that the rate of change of E at the point (x, y, z) = (2,2, -1) in the direction of (x,-1,2) is 18/5.
(b) Let ß represent the rate of change of E with respect to t along the path r(t) at t = 2. Find the value of the constant ß.
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