4. Consider the surface x² + y² - 2xy-x+3y-z=-4 at the point A(2, -3, 18). Determine the following: a. the general equation of the tangent plane to the surface at A. b. the parametric equations of the normal line to the surface at A.
4. Consider the surface x² + y² - 2xy-x+3y-z=-4 at the point A(2, -3, 18). Determine the following: a. the general equation of the tangent plane to the surface at A. b. the parametric equations of the normal line to the surface at A.
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
4 handwritten
![1. 5pts Consider the function defined by
h(x, y) = √ye.
(a) Find the domain and range of h.
(b) Draw a contour map of h for k= -1,0, 1, e.
(c) Using part (b), sketch the graph of h
2
Let function g be given by
Y
g(x, y) = = COS
(TEVE)
In(x - e)
0³g
Determine
əyəxəy
Let f(x, y) =exy and a point P(1,0)
a. Solve for the gradient of f at the point P.
b. Find the maximum and minimum rates of change of f at the point P. Then find the
direction at which these rates occur.
c. Determine the directional derivative of f at the point P in the direction of (2, 1).
Give an interpretation of the derivative obtained as a rate of change.
4.
Consider the surface x² + y² - 2xy-x+3y-z = -4 at the point A(2, -3, 18).
Determine the following:
a. the general equation of the tangent plane to the surface at A.
b. the parametric equations of the normal line to the surface at A.
5.
Given the equation xy = Arctan(ye*) where z is a function of x and y,
Əz əz
ar ду
find and
6. [
] Determine all the relative minimum and maximum values, and saddle points
(if any) of the function T defined by
T(x, y) = x² - y² + 6x - 8y + 25.
7.
Use Lagrange Multipliers to solve the following:
= 4x² + 2y² + 5
Maximize L(x, y)
subject to x² + y² = 2y.
3.
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc159504-9343-4a0c-9fca-456418f39780%2F30e9c32c-4288-40a7-9adb-ad38e715aae5%2Frirt5ma_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. 5pts Consider the function defined by
h(x, y) = √ye.
(a) Find the domain and range of h.
(b) Draw a contour map of h for k= -1,0, 1, e.
(c) Using part (b), sketch the graph of h
2
Let function g be given by
Y
g(x, y) = = COS
(TEVE)
In(x - e)
0³g
Determine
əyəxəy
Let f(x, y) =exy and a point P(1,0)
a. Solve for the gradient of f at the point P.
b. Find the maximum and minimum rates of change of f at the point P. Then find the
direction at which these rates occur.
c. Determine the directional derivative of f at the point P in the direction of (2, 1).
Give an interpretation of the derivative obtained as a rate of change.
4.
Consider the surface x² + y² - 2xy-x+3y-z = -4 at the point A(2, -3, 18).
Determine the following:
a. the general equation of the tangent plane to the surface at A.
b. the parametric equations of the normal line to the surface at A.
5.
Given the equation xy = Arctan(ye*) where z is a function of x and y,
Əz əz
ar ду
find and
6. [
] Determine all the relative minimum and maximum values, and saddle points
(if any) of the function T defined by
T(x, y) = x² - y² + 6x - 8y + 25.
7.
Use Lagrange Multipliers to solve the following:
= 4x² + 2y² + 5
Maximize L(x, y)
subject to x² + y² = 2y.
3.
+
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