lim(x趋于1)[﹙a/(1-x^2)﹢(x/(x-1)]=3/2 a等于多少

问题描述:

lim(x趋于1)[﹙a/(1-x^2)﹢(x/(x-1)]=3/2 a等于多少

lim(x→1) [a/(1-x²)]+[x/(x-1)]
=lim(x→1) [a-x(x+1)]/(1-x²)
=lim(x→1) (x²+x-a)/(x²-1)
=3/2
∵lim(x→1) x²-1=0
∴lim(x→1) x²+x-a=0
∴a=2