= Solution
Use the standard spacing convention for <machine epsilon>: the next representable <floating-point number> above $1$ is $1+2^{-40}$. In a normalized binary representation this corresponds to $41$ significant binary digits, including the leading digit. The spacing throughout $[1,2)$ is therefore $2^{-40}$.
With <rounding> to nearest, the associated <unit roundoff> is half that spacing, $u=2^{-41}$; for a normal result the relative <round-off error> is bounded by $u$. Some texts instead call $u$ machine epsilon. \b[Here $2^{-40}$ denotes the spacing scale], and the iteration counts below use that convention. It describes representation precision, not a guarantee that an arbitrarily evaluated <function> has a relative error this small.
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