结论:x→0 时,sinx=x 最好是将原式化到最后再代入用
lin(x²-sin²x)/x^4 (0/0型,有罗比达法则)
=lim(x²-sin²x)'/(x^4)'
=lim(2x-2sinxcosx)/4x³
=lim(x-sinxcosx)/2x³ (0/0型,有罗比达法则)
=lim(1-cos²x+sin²x)/6x²
=lim2sin²x/6x²
=limsin²x/3x²
=x²/3x²
=1/3
结论:x→0 时,sinx=x 最好是将原式化到最后再代入用
lin(x²-sin²x)/x^4 (0/0型,有罗比达法则)
=lim(x²-sin²x)'/(x^4)'
=lim(2x-2sinxcosx)/4x³
=lim(x-sinxcosx)/2x³ (0/0型,有罗比达法则)
=lim(1-cos²x+sin²x)/6x²
=lim2sin²x/6x²
=limsin²x/3x²
=x²/3x²
=1/3