### 1.1 Infinite Limits

Consider the function \(f\) defined by the equation \[ f(x)=\frac {1}{(x-1)^{2}} \] The graph of this function is illustrated in Figure 1.1.1.

Note that \(f\) is not defined at \(x=1\) (division by zero is not defined), but let’s consider the values of \(f\) when \(x\) is close to \(1\). Letting \(x\) approach \(1\) from both sides, the corresponding values of \(f\) are given in the following table.

\(x\) | \(f(x)\) |

0.5 | 4 |