Types of discontinuities
Limits and continuity · Mathematics
Study notes
Q: Classify the discontinuity at 0: (a) (x²−1)/(x−1) at x=1 (b) |x|/x at 0 (c) 1/x at 0 (d) sin(1/x) at 0. (a) Removable (hole; limit 2). (b) Jump (LHL −1, RHL 1). (c) Infinite (→ ±∞). (d) Oscillating (no limit, bounded oscillation).