lim x—>-2 (1/(x+2) - 12/(x^3 +8) ) 求极限~

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lim x—>-2 (1/(x+2) - 12/(x^3 +8) ) 求极限~
lim x—>-2 (1/(x+2) - 12/(x^3 +8) ) 求极限~

lim x—>-2 (1/(x+2) - 12/(x^3 +8) ) 求极限~
lim x—>-2 1/(x+2)-12/(x^3 +8)
=lim x—>-2 (x^2-2x+4)/(x^3 +8)-12/(x^3 +8)
=lim x—>-2 [x^2-2x-8]/(x^3 +8)
由于分子分母都趋向于0,所以可以用洛必达法则,上下求导.
得上式=lim x—>-2 (2x-2)/3x^2
=[2*(-2)-2]/3*(-2)^2
=-6/12
=-1/2

1/(x+2) - 12/(x^3 +8)同分
1/(x+2) - 12/(x^3 +8)=(x-4)(2+x)/(x+2)(x^2-2x+4)=(x-4)/(x^2-2x+4)
lim x->-2 (x-4)/(x^2-2x+4)=-1/2

lim x—>-2 (1/(x+2) - 12/(x^3 +8) )
=lim x—>-2 [(x^2-2x+4)-12]/(x^3 +8)
=lim x—>-2 [x^2-2x-8]/(x^3 +8)
=lim x—>-2 [(x+2)(x-4)]/[(x+2)(x^2-2x+4)]
=lim x—>-2 (x-4)/(x^2-2x+4)
=(-2-4)/(4+4+4)
=-1/2

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