高等数学极限问题

Question

需要详细解答 谢谢

Answer 1

解：
lim【x→+∞】[(x-c)/(x+c)]^x
=lim【x→+∞】[1-2c/(x+c)]^x
=lim【x→+∞】{[1-2c/(x+c)]^[-(x+c)/(2c)]}^(-2c)·lim【x→+∞】[1-2c/(x+c)]^(-c)
=e^(-2c)
所以e^(-2c)=4
得c=-(ln4)/2=-(ln2²)/2=-ln2

答案：-ln2本回答被网友采纳

Answer 2

lim[x→+∞][(x-c)/(x+c)]^x
= lim[x→+∞](1-c/x)^x/lim[x→+∞](1+c/x)^x
=lim[x→+∞][(1-c/x)^-x/c]^(-c)/lim[x→+∞][(1+c/x)^x/c]^c
=e^(-c)/e^c
=e^(-2c)
=4=e^ln4
-2c=ln4
c=-ln4/2=-ln2
应填：c=-ln2本回答被提问者采纳