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. curl( k F) = k curl 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. curl( k F) = k curl 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.
Find the domain and the derivative of the function
f (x) = In(x + Vx² -4). Enter DNE in any empty blanks.
The domain of f is:
O (-00, 0)
O (-00, a)
O (-00, a]
O (a, co)
O [a, co)
O (-00, a) U (b, c∞)
O (-00, a] U [b, 0)
O (-00, a) U (b, c)
O (-00, a] u [b, c)
O (-0, a) u (b, c]
O (-00, a] u [b, c]
O (a, b)
O (a, b]
O [a, b)
O [a, b]
O None of the Above.
a =
b =
C =
f'(x) =
OW + OW = 0 for w = f(x, y), x = u – v, and y = v –- u and demonstrate the
ди ду
6. Show that
result for w = (x – y) sin (y – x).
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*).
University Calculus: Early Transcendentals (3rd Edition)
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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