4 Let F(x, y) = 3x¹y5 - 2x³y³ + 2022. Find F · 82 F Jy² a. b. Find Give a formula for a vector that is perpendicular to the plane tangent to the surface given by F at a point (xo, yo, F(xo, yo). C. d. Give an equation for the plane tangent to the surface given by F at a point (xo, yo, F(xo, yo)). e. Write down an equation of the plane tangent to the surface described by Fat the point (0, 0, F(0,0)). How well does the z-coordinate of the point in this plane with 2 and y-coordinates equal to 1 the value of F(1,1), i.e. calculate |- F(1,1). f. Find the volume enclosed by the surface described by F, the xy-plane, the xz-plane, the yz-plane, the plane {(x, y, z) = R³|x = 1} and the plane {(x, y, z) = R³y = 1}. g. Find the volume enclosed by the surface described by F, the xz-plane, the yz-plane, the plane {(x, y, z) = R³|x = 1}, the plane {(x, y, z) = R³|y = 1} and the surface described by {(x, y, z) = R³|z = F(x, y)}.
4 Let F(x, y) = 3x¹y5 - 2x³y³ + 2022. Find F · 82 F Jy² a. b. Find Give a formula for a vector that is perpendicular to the plane tangent to the surface given by F at a point (xo, yo, F(xo, yo). C. d. Give an equation for the plane tangent to the surface given by F at a point (xo, yo, F(xo, yo)). e. Write down an equation of the plane tangent to the surface described by Fat the point (0, 0, F(0,0)). How well does the z-coordinate of the point in this plane with 2 and y-coordinates equal to 1 the value of F(1,1), i.e. calculate |- F(1,1). f. Find the volume enclosed by the surface described by F, the xy-plane, the xz-plane, the yz-plane, the plane {(x, y, z) = R³|x = 1} and the plane {(x, y, z) = R³y = 1}. g. Find the volume enclosed by the surface described by F, the xz-plane, the yz-plane, the plane {(x, y, z) = R³|x = 1}, the plane {(x, y, z) = R³|y = 1} and the surface described by {(x, y, z) = R³|z = F(x, y)}.
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:4 Let F(x, y) = 3x¹y5 - 2x³y³ + 2022.
Find F ·
82 F
b. Find Jy²
C.
a.
Give a formula for a vector that is perpendicular to the plane tangent to the
surface given by F at a point (ro, yo, F(xo, yo).
d. Give an equation for the plane tangent to the surface given by F at a point
(xo, Yo, F(xo, yo)).
e.
Write down an equation of the plane tangent to the surface described by F at
the point (0, 0, F(0,0)). How well does the z-coordinate of the point in this
plane with and y-coordinates equal to 1 the value of F(1, 1), i.e. calculate
|2 - F(1, 1).
f. Find the volume enclosed by the surface described by F, the xy-plane, the
xz-plane, the yz-plane, the plane {(x, y, z) = R³|x = 1} and the plane
{(x, y, z) = R³y = 1}.
g. Find the volume enclosed by the surface described by F, the xz-plane, the
yz-plane, the plane {(x, y, z) = R³|x = 1}, the plane {(x, y, z) = R³y = 1} and
the surface described by {(x, y, z) = R³|z = F(x, y)}.
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