a) Find the directional derivative of a(r, y) = 3-y at (1, 1) in the direction (-3,4). b) Find and classify the critical points of b(r, y) = r/3-/2-6z 1 (y 1)2 in ths derivative trsi
a) Find the directional derivative of a(r, y) = 3-y at (1, 1) in the direction (-3,4). b) Find and classify the critical points of b(r, y) = r/3-/2-6z 1 (y 1)2 in ths derivative trsi
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
Needed to be solved part a and b compelete in 20 minutes and get the thumbs up please show neat and clean work please
![a) Find the directional derivative of a(r, y) = 3r-y at (1, 1) in the direetion
(-3,4).
b) Find and classify the critical points of b(r, y) = r/3-2/2-6 1 (y - 1)
using the derivative test.
c) i) Find the Taylor scries for (1,y)= sin(r 2y) and d(r,y) = In(r 1 2y 1)
about the point (0,0), up to and including the quadratic terms.
ii) Prove the curves e and d touch tangentially at the point (0,0).
d) Let S
the right half-plane, and define :S T by
{(r, y)|1<0} C R the left half-plane, T
{(u, v) |u> 0} C R² be
i) Find J(S)
ii) Let g: S-T be defined by
Show fog(u)
iii) Hence find .(g) in Lerms of u and r by the Inverse Function Theorem.
Fu and g o f(x) x.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc2d5068-03e4-4cff-b5a4-f8e0cb916b03%2F086de115-ebde-449d-a87c-41543ba65926%2Fswbb3j8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) Find the directional derivative of a(r, y) = 3r-y at (1, 1) in the direetion
(-3,4).
b) Find and classify the critical points of b(r, y) = r/3-2/2-6 1 (y - 1)
using the derivative test.
c) i) Find the Taylor scries for (1,y)= sin(r 2y) and d(r,y) = In(r 1 2y 1)
about the point (0,0), up to and including the quadratic terms.
ii) Prove the curves e and d touch tangentially at the point (0,0).
d) Let S
the right half-plane, and define :S T by
{(r, y)|1<0} C R the left half-plane, T
{(u, v) |u> 0} C R² be
i) Find J(S)
ii) Let g: S-T be defined by
Show fog(u)
iii) Hence find .(g) in Lerms of u and r by the Inverse Function Theorem.
Fu and g o f(x) x.
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