Determine if the field Bold Upper F equals 10 yz Bold i plus 10 xz Bold j plus 10 xy Bold k is conservative or not conservative.

F is conservative if we can find a scalar funciton f such that grad(f) = F.

This would entail

Integrate both sides of the first equation with respect to x :

Differentiate both sides with respect to y :

Differentiate both sides with respect to z :

So we have

that satisfies

and so F is indeed conservative.

from the figure we get,

the x axis shows   the months and,

the y-axis shows the number of satisfied customer.

each line or each cell in upward direction (y-axis) shows 500.

the appropriate scale for the y - axis is: -

a = 2000 customers

b = 4000 customers

c = 6000 customers

d = 8000 customers

e = 10000 customers

f = 12000 customers

g = 14000 customers

go on the tube you might find some information there