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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Only part C needed in 10 minutes
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5eb4e418-6e24-4c36-a328-ddb87726da23%2Ff29edf27-ecf0-41d6-8d29-924716e8fd66%2Fqusgrsk_processed.jpeg&w=3840&q=75)
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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