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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
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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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.
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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