高数笔记：间断点的类型 By pluvet 2019年11月9日2020年4月5日 目录 第一类间断点可去间断点跳跃间断点第二类间断点无穷间断点震荡间断点第一类间断点 可去间断点 函数在该点，左极限、右极限存在且相等，但左右极限不等于该点函数值，或函数在该点无定义。 –3–3–3–2–2–2–1–1–1111222333444–3–3–3–2–2–2–1–1–1111222333444000fffAAA –2.5–2.5–2.5–2–2–2–1.5–1.5–1.5–1–1–1–0.5–0.5–0.50.50.50.51111.51.51.52222.52.52.53333.53.53.5–1.5–1.5–1.5–1–1–1–0.5–0.5–0.50.50.50.51111.51.51.52222.52.52.5333000fffAAAA'A'A' 跳跃间断点 函数在该点左极限、右极限存在，但不相等。 –3–3–3–2–2–2–1–1–1111222333444–3–3–3–2–2–2–1–1–1111222333444000fffAAABBB –0.5–0.5–0.50.50.50.51111.51.51.52222.52.52.53333.53.53.54444.54.54.5555–1.5–1.5–1.5–1–1–1–0.5–0.5–0.50.50.50.51111.51.51.52222.52.52.53333.53.53.54444.54.54.5555000gggAAA 第二类间断点 无穷间断点 –3–3–3–2–2–2–1–1–1111222333444–3–3–3–2–2–2–1–1–1111222333444000 震荡间断点 –1–1–1–0.8–0.8–0.8–0.6–0.6–0.6–0.4–0.4–0.4–0.2–0.2–0.20.20.20.20.40.40.40.60.60.60.80.80.81111.21.21.2–1–1–1–0.8–0.8–0.8–0.6–0.6–0.6–0.4–0.4–0.4–0.2–0.2–0.20.20.20.20.40.40.40.60.60.60.80.80.8111000fff