(a) limx→1x2 − 1x − 1

The given expression is in the form of 0/0 when x approaches 1, which is an indeterminate form. We can use L'Hopital's rule or simplify the expression. Here, I'll simplify the expression:

x^2 - 1 = (x - 1)(x + 1) (This is a difference of squares)

So, the expression becomes:

lim (x→1) (x - 1)(x + 1) / (x - 1)

We can cancel out the (x - 1) terms:

lim (x→1) (x + 1)

Now, substitute x = 1:

1 + 1 = 2

So, lim (x→1) (x^2 - 1) / (x - 1) = 2.