v = x^3
dv = 3 x^2 dx agrred
dv/v *100 = percent error in volume
dv/v = 3 x^2/x^3 dx
but dx/x * 100 = percent error in side
dv/v = 3 dx/x
so
dv/v * 100 = 3 dx/x * 100
= 3 * 2% = 6 percent
if the sides of a cube are measured with an error of 2% use differentials to estimate the relative error in the volume
df= 3x^2 * dx
df= 3x^2 * 1/50
df= 3/50*x^2
is this right?
2 answers
Thank you!! :-)