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.
Find the first and the second derivatives of the function
where a is a parameter (1.e. a real number)
Also calculate the exact values of f' (z) and f"(z) at z = 0.
(HINT. simplify the function before calculating the derivatives)
Find the direction in which the function increase and decrease most rapidly
at point Po. Then find the derivative of the function in that direction.
f(x,y z) =
|- yz
„P.(4, 1,1)
Let r =.
Compute the derivative.
(Use symbolic notation and fractions where needed. Give your answer in the form of comma separated list of i, j, k components.)
dr
dt
> help (fractions)
Chapter 15 Solutions
Calculus Early Transcendentals, Binder Ready Version
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