lim(x→1)[(x^(3x-2)-x)sin2(x-1)]/(x-1)^3
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lim(x→1)[(x^(3x-2)-x)sin2(x-1)]/(x-1)^3
lim(x→1)[(x^(3x-2)-x)sin2(x-1)]/(x-1)^3
lim(x→1)[(x^(3x-2)-x)sin2(x-1)]/(x-1)^3
令t=x-1,则t→0
lim【x→1】{[x^(3x-2)-x]·sin2(x-1)}/(x-1)³
=lim【t→0】{[(t+1)^(3t+1)-(t+1)]·sin2t}/t³
=lim【t→0】{[(t+1)^(3t+1)-(t+1)]·2t}/t³
=2lim【t→0】[(1+t)^(3t+1)-1-t]/t² →利用等价无穷小代换x→0时,(1+x)^a-1~ax
=2lim【t→0】[t(3t+1)-t]/t²
=2lim【t→0】3t²/t²
=2×3
=6
用无穷小等量代换
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