微积分问题:6道计算题,如图所示.
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微积分问题:6道计算题,如图所示.
![](http://img.wesiedu.com/upload/c/08/c08db06ec59f67f640ca319e9fa8ff42.jpg)
![](http://img.wesiedu.com/upload/c/08/c08db06ec59f67f640ca319e9fa8ff42.jpg)
![微积分问题:6道计算题,如图所示.](/uploads/image/z/17480251-19-1.jpg?t=%E5%BE%AE%E7%A7%AF%E5%88%86%E9%97%AE%E9%A2%98%EF%BC%9A6%E9%81%93%E8%AE%A1%E7%AE%97%E9%A2%98%2C%E5%A6%82%E5%9B%BE%E6%89%80%E7%A4%BA.)
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
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