Evaluate $\lim\limits_{y\to 0}\log(1+y)/y$ without LHR or Taylor series Problem 12 on p. 297 of Spivak's Calculus (first edition) is 

Find $\lim\limits_{y\to 0}\log (1+y)/y$. (You can use L'Hospital's
  rule, but that would be silly.)

I'm not sure the other method he's looking for besides LHR. I can also think of expanding $\log(1+y)$ in Taylor series, but this is before the section of the book on Taylor series.

$$
\lim_{y\to 0} \frac{\log(1+y)}{y} = \lim_{y\to 0} \log(1+y)^{1/y} = \log \lim_{y\to 0} (1+y)^{1/y} = \log e = 1
$$
