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I'm having trouble with this maths question and was wondering if someone could help me?? The question asks:

The electrical resistance R of a wire is given by

k / r^2 where k = constant, r = radius of wire.

Use differentials to estimate the percentage error in the measured value of r if we want the percentage error in R to be within +/- 3%.

I'm really not sure if this is the right approach... please help me...

Using the method of linear approx. i have...

ΔR = R(r + Δr) - R(r)

~ (dR(r) / dr) * ( Δr )

I know...

R = k / r^2

dR/dr = -2*k*( r^-3 )

and therefore...

ΔR = -2*k*( r^-3 ) * ( Δr )

So i'm thinking to increase R by 3% i need...

ΔR / R(r) = 0.03

but after substituting everything in i get Δr = 0.03??

please i really need help!!