Question 1 Consider f(r, y) = –1+ + r-1)2 g 08) a) Draw the level sets (or say why you cannot) of ƒ(x, y) = k for k =-1, 0, 3. Clearly label each level curve and indicate at least one point one each curve.
Question 1 Consider f(r, y) = –1+ + r-1)2 g 08) a) Draw the level sets (or say why you cannot) of ƒ(x, y) = k for k =-1, 0, 3. Clearly label each level curve and indicate at least one point one each curve.
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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Transcribed Image Text:Question 1
Consider f(x, y) = –1+ +
og 0) C mdo
a) Draw the level sets (or say why you cannot) of f(x, y) = k for k = -1, 0, 3.
Clearly label each level curve and indicate at least one point one each curve.
b) At each of the points where the k = 3 level curve intersects the y-axis,
draw a vector u in the direction the function f is increasing fastest.
) At each of the points where thek=1 level curve intersects the x-axis,
draw a vetor v such that the directional derivative of f at this point in the direction
of v is zero.
lov Inmiat bas lamizem isdely edi bri (etaiog 0I) (d)
d), Compute the directional derivative of f(x, y) at (x, y) = (1,3) in the
(-1,-3).
direction w=
verors
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Consider the given function:
The objective is to draw the level sets of for .
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