Question

文科高数题目lim[1/(x+1)-3/(x^3+1)] x趋向于-1 lim[(e^2x-1)/x] x趋向于0 没学

Answer 1

1/(x+1)-3/(x^3+1)

=[(x^2-x+1)-3]/(x^3+1)

=(x^2-x-2)/(x^3+1)

=(x-2)(x+1)/(x+1)(x^2-x+1)

=(x-2)/(x^2-x+1)

所以lim(x→-1)[1/(x+1)-3/(x^3+1)]

=lim(x→-1)(x-2)/(x^2-x+1)

=(-1-2)/(1+1+1)

=-1

当x趋向于0时,e^(2x)-1和x趋于0

是0/0型,可以用洛必达法则

lim(x→0)[(e^2x-1)/x]

=lim(x→0)2e^2x

=2