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a^3-b^3 = (a-b)(a^2+ab+b^2)
a= x^(1/3) , b=1
x-1
=[ x^(1/3) -1 ]. [ x^(2/3) +x^(1/3) +1 ]
lim(x->1) [ x^(1/3) -1 ]/(x-1)
=lim(x->1) [ x^(1/3) -1 ]/ { [ x^(1/3) -1 ]. [ x^(2/3) +x^(1/3) +1 ] }
=lim(x->1) 1/ [ x^(2/3) +x^(1/3) +1 ]
=1/(1+1+1)
=1/3
a= x^(1/3) , b=1
x-1
=[ x^(1/3) -1 ]. [ x^(2/3) +x^(1/3) +1 ]
lim(x->1) [ x^(1/3) -1 ]/(x-1)
=lim(x->1) [ x^(1/3) -1 ]/ { [ x^(1/3) -1 ]. [ x^(2/3) +x^(1/3) +1 ] }
=lim(x->1) 1/ [ x^(2/3) +x^(1/3) +1 ]
=1/(1+1+1)
=1/3
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