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using the derivative test. c) i) Find the Taylor series for c(r, y) = sin(r + 2y) and d(r, y) = In(+ 2y + 1) about the point (0,0), up to and including the quadratic terms. ii) Prove the curves c and d touch tangentially at the point (0,0).

using the derivative test. c) i) Find the Taylor series for c(r, y) = sin(r + 2y) and d(r, y) = In(+ 2y + 1) about the point (0,0), up to and including the quadratic terms. ii) Prove the curves c and d touch tangentially at the point (0,0).

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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a) Find the directional derivative of a(r, y) (-3, 4). b) Find and classify the critical points of b(r, y) = r'/3 – /2 - 6x + (y – 1)? using the derivative test. = 3r2 y* at (1, 1) in the direction %3D c) i) Find the Taylor series for c(r, y) = sin(r + 2y) and d(r, y) = In(r +2y + 1) about the point (0,0), up to and including the quadratic terms. ii) Prove the curves c and d touch tangentially at the point (0,0).
Transcribed Image Text:a) Find the directional derivative of a(r, y) (-3, 4). b) Find and classify the critical points of b(r, y) = r'/3 – /2 - 6x + (y – 1)? using the derivative test. = 3r2 y* at (1, 1) in the direction %3D c) i) Find the Taylor series for c(r, y) = sin(r + 2y) and d(r, y) = In(r +2y + 1) about the point (0,0), up to and including the quadratic terms. ii) Prove the curves c and d touch tangentially at the point (0,0).
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