求极限,说一下方法,和过程!
3个回答
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lim(x->-1) [ 1/(x+1) - 3/(x^3+1) ]
=lim(x->-1) { 1/(x+1) - 3/[(x+1)(x^2-x+1) ] }
=lim(x->-1) [ (x^2-x+1) -3 ]/[(x+1)(x^2-x+1) ]
=lim(x->-1) (x^2-x -2)/[(x+1)(x^2-x+1) ]
=lim(x->-1) (x+1)(x-2)/[(x+1)(x^2-x+1) ]
=lim(x->-1) (x-2)/(x^2-x+1)
=(-1-2)/(1+1+1)
=-1
=lim(x->-1) { 1/(x+1) - 3/[(x+1)(x^2-x+1) ] }
=lim(x->-1) [ (x^2-x+1) -3 ]/[(x+1)(x^2-x+1) ]
=lim(x->-1) (x^2-x -2)/[(x+1)(x^2-x+1) ]
=lim(x->-1) (x+1)(x-2)/[(x+1)(x^2-x+1) ]
=lim(x->-1) (x-2)/(x^2-x+1)
=(-1-2)/(1+1+1)
=-1
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