Question

differentials help!
Volume of a cube = s^3, s=10, ds=0.1
i need to find the estimated dV and the actual ΔV.
i dont know what it means.

Answer 1

\[V=s ^{3}\]\[dV=3s ^{2}\times(ds)\]

Solve for ds by plugging in other values, so set ds on one side and the other variables on the other side:

\[dV/(3s ^{2}) = ds\]

Answer 2

V = Volume fo the Cube
s = measure of one edge of the cube,

\(V(s) = s^{3}\)

\(\dfrac{dV}{ds} = 3s^{2}\) or \(dV = 3s^{2}\cdot ds\)

Are we getting anywhere? The notation may be new.

Answer 3

I'm pretty sure I have never seen ds=.1, since that doesn't make a whole lot of sense.

Answer 4

idk.. this is the problem my teacher gave me.

Answer 5

ds means change in side length per time.

Answer 6

No, ds doesn't mean that, ds/dt means that.

Answer 7

ok soo dV = 3s^2ds
now how do i find ΔV? what does that even mean?

Answer 8

Change in volume.

Answer 9

wait is dV and ΔV the same thing?

Answer 10

I've done calculus for about 2 years and I have never seen a problem like this, simply because it is nonsensical.

Answer 11

ds is an infinitesimal, not a real number, plain and simple. It would be like saying infinity=90billion, solve.