lim(x→0)(x²-sin²x)/x^4
=lim(x→0)(x+sinx)(x-sinx)/x^4
=lim(x→0)(x+sinx)x³/6x^4
=1/6*lim(x→0)(x+sinx)/x
=1/6*(1+1)
=1/3
lim(x→0)(x²-sin²x)/x^4
=lim(x→0)(2x-2sinxcosx)/4x³
=lim(x→0)(2x-sin2x)/4x³
=lim(x→0)(2-2cos2x)/12x²
=lim(x→0)(1-cos2x)/6x²
=lim(x→0)2sin2x/12x
=lim(x→0)2cos2x/6
=1/3
等价替换也好洛必达法则也好都是1/3,你是怎麼算错的?
你自己计算错了！sin²x的导数不是cos²x，而是2sinxcosx
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