Question

微积分问题：6道计算题,如图所示.

Answer 1

1.原式=lim(x→1)(x^3-x^2+x^2-x-2x+2)/(x^3-x^2-x+1)=lim(x→1)(x^2(x-1)+x(x-1)-2(x-1))/(x^2(x-1)-(x-1))=lim(x→1)(x^2+x-2)/(x^2-1)=lim(x→1)[(x+2)(x-1)]/[(x+1)(x-1)]=lim(x→1)(x+2)/(x+1)=3/2

2.两边对x求导：y+xy'=e^(x+y)*(1+y')

y+xy'=e^(x+y)+y'e^(x+y)

y'(x-e^(x+y))=e^(x+y)-y

y'=(e^(x+y)-y)/(x-e^(x+y))

3.因为0