We want to find a scalar function

such that

.
So we need to have

Integrating both sides with respect to

gives

Differentiating with respect to

gives



So we find that

By the fundamental theorem of calculus, we then know the line integral depends only on the values of

at the endpoints of the path. Therefore

As

, the sequence

converges to zero.
If you're talking about the infinite series

well we've shown by comparison that this series must also converge because we know any geometric series

will converge as long as

.
Answer:
y = 3/2*x - 5
Step-by-step explanation:
Lets say that P1=(6,4) and P2=(4,1) and that the form of the equation must be y=m*x+b where m is the slope and b the independent variable. Then having two given points we can use the slope formula to find the slope value as:
P1=(x1,y1) and P2=(x2,y2)
slope formula ---> m=(y2-y1)/(x2-x1)
Replacing the given points ---> m=(1-4)/(4-6) = 3/2
then replacing the slope value obtained:
y = 3/2*x + b
Now lets find the value of b. For this we have to replace in the equation a point it can be P1 or P2, i will replace P2:
1 = 3/2*4 + b
1 = 6 + b
1 - 6 = b
-5 = b
therefore the line equation is:
y = 3/2*x - 5
Answer:
64
Step-by-step explanation:
surface area of the cube =96
suppose one side of the cube = a
volume of the cube(V) =?
surface area = 6a^2
6a^2=96
a
^2
=96/6
a^2=16
a = 4
SO
V=
a^
3
V=64.
brainliest plz :'D