几道高数极限问题,求正确答案,最好有过程?
发布网友
发布时间：2022-05-29 10:39
共1个回答
热心网友
时间：2023-10-16 00:50
lim(x—>1)(1-x)/x＝(1-1)/1＝0/1＝0，
所以
lim(x—>1)x/(1-x)＝∞；
(2) lim(x—>1)(x²-1)/(x-1)²
＝lim(x—>1)(x+1)(x-1)/(x-1)²
＝lim(x—>1)(x+1)/(x-1)
＝∞；
(3) lim(x—>1)[1/(1-x)-3/(1-x³)]
＝lim(x—>1)[(1+x+x²)/(1-x³)-3/(1-x³)]
＝lim(x—>1)[(x²+x-2)/(1-x³)]
＝lim(x—>1)[(x-1)(x+2)/(1-x³)]
＝lim(x—>1)[(x+2)/(1+x+x²)]
＝(1+2)/(1+1+1²)
＝1；
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