如下
a^3-b^3 = (a-b)(a^2+ab+b^2)
x-8=[ x^(1/3) -2 ].[ x^(2/3) +2x^(1/3) +4 ]
/
lim(x->8) [√(9+2x) -5 ]/[ x^(1/3) -2 ]
=lim(x->8) [(9+2x) -25 ]/{ [ x^(1/3) -2 ] . [√(9+2x) +5 ] }
=2lim(x->8) (x-8)/{ [ x^(1/3) -2 ] . [√(9+2x) +5 ] }
=2lim(x->8) [ x^(1/3) -2 ].[ x^(2/3) +2x^(1/3) +4 ] /{ [ x^(1/3) -2 ] .[√(9+2x) +5 ] }
=2lim(x->8) [ x^(2/3) +2x^(1/3) +4 ] /[√(9+2x) +5 ]
=2 ( 4 +4 +4 ) /[√(9+16) +5 ]
=12/5
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