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
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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
没学过罗比达法则..
lim[1/(x+1)-3/(x^3+1)] x趋向于-1
lim[(e^2x-1)/x] x趋向于0
没学过罗比达法则..
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
=[(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
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
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