«高数考点:间断点的类型»
by pluvet on Nov 9, 2019

高数考点:间断点的类型


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

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