lim(x→0）sin3x/tan2x（用等价无穷小代换）
＝lim(x→0）3x/2x
=3/2
lim(x→∞）[(2x-1)/(2x+2)]^x
=lim(x→∞）[(2x+2-3)/(2x+2)]^x
=lim(x→∞）[1-3/(2x+2)]^x
=lim(x→∞）[1-3/(2x+2)]^(-2x/3*-3/2)
=e^(-3/2)
两端对x求导得
2yy'+y+xy'-1=0
y'=(1-y)/(x+2y)
lim(x→0）sin3x/tan2x（用等价无穷小代换）
＝lim(x→0）3x/2x
=3/2
lim(x→∞）[(2x-1)/(2x+2)]^x
=lim(x→∞）[(2x+2-3)/(2x+2)]^x
=lim(x→∞）[1-3/(2x+2)]^x
=lim(x→∞）[1-3/(2x+2)]^(-2x/3*-3/2)
=e^(-3/2)
两端对x求导得
2yy'+y+xy'-1=0
y'=(1-y)/(x+2y)