1-8高等數(shù)學(xué)課后習(xí)題答案

1、習(xí)題1?81?研究下列函數(shù)的連續(xù)性?并畫出函數(shù)的圖形?(1)??????????21210)(2xxxxxf解已知多項(xiàng)式函數(shù)是連續(xù)函數(shù)?所以函數(shù)f(x)在[0?1)和(1?2]內(nèi)是連續(xù)的?在x?1處?因?yàn)閒(1)?1?并且??1lim)(lim211??????xxfxx1)2(lim)(lim11???????xxfxx所以?從而函數(shù)f(x)在x?1處是連續(xù)的?1)(lim1??xfx綜上所述，函數(shù)f(x)在[0?2]上是連續(xù)函數(shù)?(

2、2)?????????1||111)(xxxxf解只需考察函數(shù)在x??1和x?1處的連續(xù)性?在x??1處?因?yàn)閒(?1)??1?并且?)1(11lim)(lim11??????????fxfxx?)1(1lim)(lim11???????????fxxfxx所以函數(shù)在x??1處間斷?但右連續(xù)?在x?1處?因?yàn)閒(1)?1?并且?f(1)??f(1)?1lim)(lim11??????xxfxx11lim)(lim11??????xxxf

3、所以函數(shù)在x?1處連續(xù)?綜合上述討論?函數(shù)在(????1)和(?1???)內(nèi)連續(xù)?在x??1處間斷?但右連續(xù)?解因?yàn)楹瘮?shù)在x?0處無定義?所以x?0是函數(shù)xy1cos2?的間斷點(diǎn)?又因?yàn)椴淮嬖?所以x?0是函數(shù)的第xy1cos2?xx1coslim20?二類間斷點(diǎn)?(4)?x?1?????????1311xxxxy解因?yàn)??所以x?10)1(lim)(lim11???????xxfxx2)3(lim)(lim11???????xxfxx

4、是函數(shù)的第一類不可去間斷點(diǎn)?3?討論函數(shù)的連續(xù)性?若有間斷點(diǎn)?判別其類xxxxfnnn2211lim)(?????型?解????????????????1||1||01||11lim)(22xxxxxxxxxfnnn在分段點(diǎn)x??1處?因?yàn)?1)(lim)(lim11?????????xxfxx?所以x??1為函數(shù)的第一類不可去間斷點(diǎn)?1lim)(lim11?????????xxfxx在分段點(diǎn)x?1處?因?yàn)??1lim)(lim11??