en is the function h(x, y) = (y − 1)(x + 1). Draw the level curves for h(x, y) = c for c = -1, 0, 1 in the xy-plane. Label curves clearly with the appropriate value of c. Show all your working. In the drawing of the previous part, clearly mark points P₁ = (-1/2,3), (6) -1). Draw a direction in which h neither increases nor decreases at P₁. Draw the gradient vector of h at P₂. Draw the direction of the steepest decrease at P3. Show djustify your choices P₁ = (-1, 1) and P₁ = P3 (-
en is the function h(x, y) = (y − 1)(x + 1). Draw the level curves for h(x, y) = c for c = -1, 0, 1 in the xy-plane. Label curves clearly with the appropriate value of c. Show all your working. In the drawing of the previous part, clearly mark points P₁ = (-1/2,3), (6) -1). Draw a direction in which h neither increases nor decreases at P₁. Draw the gradient vector of h at P₂. Draw the direction of the steepest decrease at P3. Show djustify your choices P₁ = (-1, 1) and P₁ = P3 (-
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hi, I have a multivariable calculus question. Thanks.
Transcribed Image Text:(a) Given is the function h(x, y) = (y − 1)(x + 1).
(i) Draw the level curves for h(x, y) = c for c = -1, 0, 1 in the xy-plane. Label curves clearly with
the appropriate value of c. Show all your working.
(ii) In the drawing of the previous part, clearly mark points P₁ = (-1,3),
1
1
, 1) and P3 = (– -1). Draw a direction in which h neither increases nor decreases
2
P₂ = (-
at P₁. Draw the gradient vector of h at P₂. Draw the direction of the steepest decrease at P3. Show
your working and justify your choices.
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