幾種常見類型.
可去間斷點(diǎn)：函數(shù)在該點(diǎn)左極限、右極限存在且相等,但不等于該點(diǎn)函數(shù)值或函數(shù)在該點(diǎn)無定義.如函數(shù)y＝（x^2-1)/(x-1)在點(diǎn)x＝1處.
跳躍間斷點(diǎn)：函數(shù)在該點(diǎn)左極限、右極限存在,但不相等.如函數(shù)y＝|x|/x在點(diǎn)x＝0處.
無窮間斷點(diǎn)：函數(shù)在該點(diǎn)無定義,且左極限、右極限至少有一個(gè)為∞.如函數(shù)y＝tanx在點(diǎn)x＝π/2處.
振蕩間斷點(diǎn)：函數(shù)在該點(diǎn)無定義,當(dāng)自變量趨于該點(diǎn)時(shí),函數(shù)值在兩個(gè)常數(shù)間變動(dòng)無限多次.如函數(shù)y＝sin(1/x)在x＝0處.
可去間斷點(diǎn)和跳躍間斷點(diǎn)稱為第一類間斷點(diǎn),也叫有限型間斷點(diǎn).
其它間斷點(diǎn)稱為第二類間斷點(diǎn).
x=0是函數(shù)f(x)=ln(1+x)/x的【無窮間或第二類】間斷點(diǎn)