Mathematics for Electrical Engineering and Computing

L'Hopital's rule

When sketching graphs of functions in Chapter 11, we looked at graphs where the function is undefined for some values of x. The function f (x) = 1/ x, for instance, is not defined when x = 0 and tends to −∞ as x → 0 and tends to $+\infty$ as x → 0⁺. Not all functions that have undefined points tend to $\pm \infty$ near the point where they are undefined. For example, consider the function f (x) = sin (x) / x. The graph of this function is shown in Figure 12.5. The function is not defined for x = 0, which we can see by substituting x = 0 into the function ...