lim x—>-2 (1/(x+2) - 12/(x^3 +8) ) 求极限~
问题描述：
lim x—>-2 (1/(x+2) - 12/(x^3 +8) ) 求极限~
答
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
答
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
答
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*(...