计算极限 lim(sin3x/sin5x) x趋近于0 lim[2x²/（1-cosx)]x趋近于0文科····
问题描述：
计算极限 lim(sin3x/sin5x) x趋近于0 lim[2x²/（1-cosx)]x趋近于0
文科····
答
1. lim[ sin(3x)/sin(5x) , x->0] 等价无穷小代换
= lim[ 3x /(5x), x->0] = 3/5
2. lim[ 2x²/(1-cosx) , x->0] 等价无穷小代换
= lim[ 2x² / (x²/2) , x->0]
=4
或： 原式= lim[ 4x / sinx, x->0] 罗必塔法则
=4
答
lim(sin3x/sin5x) x趋近于0
=lim3/5(5xsin3x/3xsin5x) x趋近于0
=3/5
lim[2x²/（1-cosx)]x趋近于0
=lim[2x²/（2sin^x)]x趋近于0
=1