Let k be a constant, F = F( x , y , z ) , G = G( x , y , z ) , and ϕ = ϕ ( x , y , z ) . Prove the following identities, assuming that all derivatives involved exist and are continuous. div( k F) = k div F
Let k be a constant, F = F( x , y , z ) , G = G( x , y , z ) , and ϕ = ϕ ( x , y , z ) . Prove the following identities, assuming that all derivatives involved exist and are continuous. div( k F) = k div F
Let k be a constant,
F
=
F(
x
,
y
,
z
)
,
G
=
G(
x
,
y
,
z
)
,
and
ϕ
=
ϕ
(
x
,
y
,
z
)
.
Prove the following identities, assuming that all derivatives involved exist and are continuous.
Consider the following function which is defined for all x and y:
f(x, y) = 2(1-p²)x²y² - x² - y² + 3pxy + 2x+4y+2
where p is a constant.
(a) Find the first order derivatives of f and enter them as functions of x, y and p
(b) Find the second order derivatives of f and enter them as functions of x, y and p
(c) For p = 1, find the stationary point (x*, y*).
Chapter 15 Solutions
Calculus Early Transcendentals, Binder Ready Version
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY