
Let

The curl is

where
denotes the partial derivative operator with respect to
. Recall that



and that for any two vectors
and
,
, and
.
The cross product reduces to

When you compute the partial derivatives, you'll find that all the components reduce to 0 and

which means
is indeed conservative and we can find
.
Integrate both sides of

with respect to
and

Differentiate both sides with respect to
and




Now

and differentiating with respect to
gives




for some constant
. So

Answer:
Multiply by 2 because if 6÷3=2, same for 24÷12=2
Answer:
(a) rate of change = 8
(b) Function: y = 8x
(c) Domain: 0 ≤ x ≤ 2
Range: 0 ≤ y ≤ 16
Explanation:
Looks like a inverse variation sequence.
Inverse Variation formula: y = k(x)
Take two points: (1, 8), (2, 16)
Find the value of k which is constant also considered as <u>rate of change</u>.
<u>Insert values</u>:
===========
Equation: y = 8x
Domain lies in the x axis, Range lies in the y axis.