Domains of functions of three or more variables Find the domain of the following functions. If possible, give a description of the domains ( for example, all points outside a sphere of radius 1 centered at the origin ) . 51. F ( x , y , z ) = y − x 2
Domains of functions of three or more variables Find the domain of the following functions. If possible, give a description of the domains ( for example, all points outside a sphere of radius 1 centered at the origin ) . 51. F ( x , y , z ) = y − x 2
Solution Summary: The author explains that the domain of the function F(x,y,z)=sqrty-x2 includes all points of R3
Domains of functions of three or more variablesFind the domain of the following functions. If possible, give a description of the domains (for example, all points outside a sphere of radius 1 centered at the origin).
Sketch a contour map of the function.
f(x, y) = x²
+9y²
y
X
(Write an equation for the cross section at z = 4 using
and y.)
(Write an equation for the cross section at z = 9 using x and y.)
(Write an equation for the cross section at y = 0 using x and z.)
y
Sketch the graph of the function and compare it to the contour map. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)
(Write an equation for the cross section at z = 2 using x and y.)
(Write an equation for the cross section at x = 0 using y and z.)
X
y
X
y
X
Consider an axisymmetric feeding bowl as shown on the left below. Its cross-section is shown on the right with the axis of symmetry aligned along the y-axis.
The top curve of the cross-section is given by the function
b. What is the capacity of this bowl?
Capacity=
cm³
c. Find the volume of water inside the bowl if the water level is 3.3 cm measured from the bottom.
Volume of water =
1
961
y =
C
961
The horizontal base joins the endpoints of the top curve. Both x and y are in cm.
You may need to use a computer algebra system to solve some of the following problems. Round all your answers to at least 3 significant figures.
a. Assume that the bowl is solid and is made with plastic. Find the amount of plastic (as a volume) required to make this bowl.
Amount of plastic =
cm³
cm3
-x4 (9-x)
1 4
-x¹ (9 + x)
y
0≤x≤9.1
-9.1 < x < 0
X
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY