Final answer:
The statement is true because an indeterminate form like 0/0 or ∞/∞ does not always signify a vertical asymptote; it simply indicates that the limit needs further analysis to be determined.
Step-by-step explanation:
The statement 'when a limit involves an indeterminate form, x=c may not be its vertical asymptote' is true. An indeterminate form, like ∞/∞ or 0/0, does not guarantee the presence of a vertical asymptote at x=c. It means the limit at that point is not immediately determinable and requires further analysis, such as algebraic manipulation or applying L'Hôpital's Rule, to find the limit. A vertical asymptote occurs when the values of a function increase without bound as it approaches a certain value of x, but an indeterminate form may resolve to a finite limit or still be undefined after such manipulations, not necessarily implying an asymptote.
As a demonstration using the function y = 1/x, as depicted in Figure 4.4, x=0 is indeed a vertical asymptote because as x approaches 0, y approaches infinity. However, a function such as (sinx)/x, has an indeterminate form at x=0, but it is well known that the limit as x approaches 0 is 1, and there is no vertical asymptote at that point.