What does `lim_(x to 1) (x^(2)-1)/(x+1)` equal ?

Explanation

Since `(x^(2)-1)/(x+1)` reduces to `x-1`,
`lim_(x to 1)(x^(2)-1)/(x+1)=lim_(x to 1) x-1=0`
Although the window settings on your calculator may not make it possible to see the hole at `x=1`, you can determine the limit of this function as x approaches 1 from both sides by using the table feature. Select Ask for Indpnt, go to TABLE, enter values of x that get progressively closer to 1 from below (e.g., 0.9, 0.99, 0.999, 0.999, etc.) and above (e.g., 1.1, 1.01, 1.001, etc.), and watch y get closer to 1.