posted by Joe .
Use linear approximation, i.e. the tangent line, to approximate (1/0.504) as follows: Find the equation of the tangent line to f(x)=1/x at a "nice" point near 0.504. Then use this to approximate (1/0.504).
The idea behind the approximation is:
y(x) = y(x0)+y'(x0)*Δx
=y(x)-Δx / (x0 ²)
Now apply x0=0.5, Δx=0.004
compare to approximate actual value of