Question 2 For parts a), b) and c) let f(x, y) = x² – 3xy. a) At the point with x = 1 and y = -1 compute the unit vector pointing in the direction of greatest increase of the function f(x, y) and compute the rate of increase in that direction. b) Compute an equation for the plane tangent to the surface given by the equation = f(x, y) at the point in space with x = 1 and y = -1. c) Find the rate at which f(x, y) is changing at (1,-1) in the direction toward the point (5,2).
Question 2 For parts a), b) and c) let f(x, y) = x² – 3xy. a) At the point with x = 1 and y = -1 compute the unit vector pointing in the direction of greatest increase of the function f(x, y) and compute the rate of increase in that direction. b) Compute an equation for the plane tangent to the surface given by the equation = f(x, y) at the point in space with x = 1 and y = -1. c) Find the rate at which f(x, y) is changing at (1,-1) in the direction toward the point (5,2).
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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Question 1 Compute the limit
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Instructions: Show your work. If you use a theorem or a test to help solve a problem,
state the name of the theorem or test.
+
발
a
X +
1 of 2
99+
lim
(x,y) → (0,0)
CD
=
Question 2 For parts a), b) and c) let f(x, y) = x² – 3xy.
a) At the point with x = 1 and y −1 compute the unit vector pointing in the
direction of greatest increase of the function f(x, y) and compute the rate of increase
in that direction.
b) Compute an equation for the plane tangent to the surface given by the equation
z = f(x, y) at the point in space with x = 1 and y = −1.
c) Find the rate at which f(x, y) is changing at (1,−1) in the direction toward the
point (5,2).
= X Y =
9
Question 3 Let E be the solid bounded by y
= x, x = Z,
mass density is given by p(x, y, z) = x. Sketch E and find its mass.
Р O
2
x³y² + 2y³
x³ +y³
or prove that it does not
J
and 2 =
= 0 whose
Earn...
60
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(4)
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12:18 PM
5/18/2023
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a
+
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