What is the limit of (x² + 1) / (x + 1) as x approaches -1?
Q1. What is the limit of (x² + 1) / (x + 1) as x approaches -1?
Answer: 2
Explanation: Factor the numerator and cancel (x + 1) to get lim (x→-1) (x - 1) + 2 / (x + 1), but since the numerator doesn't factor nicely, directly substitute to check if it's defined, getting 2 / 0, so check if L'Hopital applies or simplify: (x² + 1) / (x + 1) = ((x + 1)(x - 1) + 2) / (x + 1) = x - 1 + 2 / (x + 1). As x approaches -1, the expression approaches 2.