Question

determine the point where f has limits and the point where f does not has limits.
f(x) = 0, where x belongs to q and,
f(x) = 1/q, where x belongs to p/q​

Answer 1

Answer:

We begin our exploration of limits by taking a look at the graphs of the functions

f(x)=\frac{x^2-4}{x-2}, \, g(x)=\frac{|x-2|}{x-2}, and h(x)=\frac{1}{(x-2)^2},

Step-by-step explanation:

2 and x= -1 for x < 2. There are open circles at both endpoints (2, 1) and (-2, 1). The third is h(x) = 1 / (x-2)^2, in which the function curves asymptotically towards y=0 and x=2 in quadrants one and two." width="975" height="434"> Figure 1. These graphs show the behavior of three different functions around x=2.

Each of the three functions is undefined at x=2, but if we make this statement and no other, we give a very incomplete picture of how each function behaves in the vicinity of x=2. To express the behavior of each graph in the vicinity of 2 more completely, we need to introduce the concept of a limit.