Evaluate the limit as x approaches 1 of (x^2 - 1)/(x - 1).

Evaluate the limit as x approaches 1 of (x^2 - 1)/(x - 1).

• A. 1
• B. 2
• C. 0
• D. -2

Answer: (B)

When a limit presents what looks like an indeterminate 0/0 form, look for algebraic simplifications that remove the troublesome factor. Here the numerator factors as x^2 - 1 = (x - 1)(x + 1). For x not equal to 1, the expression simplifies to (x - 1)(x + 1)/(x - 1) = x + 1. So as x approaches 1, the expression behaves like x + 1 and tends to 2. Therefore, the limit is 2. The original expression isn’t defined at x = 1, but the limit uses values near 1, where the simplified form applies.

When a limit presents what looks like an indeterminate 0/0 form, look for algebraic simplifications that remove the troublesome factor. Here the numerator factors as x^2 - 1 = (x - 1)(x + 1). For x not equal to 1, the expression simplifies to (x - 1)(x + 1)/(x - 1) = x + 1. So as x approaches 1, the expression behaves like x + 1 and tends to 2. Therefore, the limit is 2. The original expression isn’t defined at x = 1, but the limit uses values near 1, where the simplified form applies.