Important Limits

For some limits the individual result matters less than the general principle it produces, and those principles are the ground floor for every computation that follows. This chapter derives the two families worth memorising: the trigonometric limits (the $\sin x / x$ type and its variants) and the exponential-logarithmic limits (the $(1+x)^{1/x}$ type), then shows how they are actually used in equivalent-infinitesimal substitution and in evaluating power-exponential expressions.