帮我求下列极限:lim(x趋向于0)sin5x/3x;

帮我求下列极限:lim(x趋向于0)sin5x/3x;
帮我求下列极限:lim(x趋向于0)sin5x/3x;

帮我求下列极限:lim(x趋向于0)sin5x/3x;
令5x＝y,最后结果为5/3

上下除以x
=(sin5x/x)/(sin3x/x)
=5(sin5x/5x)/[3(sin3x/3x)]
x趋向于0则5x趋向于0，3x趋向于0
所以sin5x/5x和sin3x/3x极限都是1
所以原来极限=5/3

x趋于0时，5x也是趋于0，
lim sin5x/3x=lim sin5x/(5x*(3/5))=(5/3)lim sin5x/5x=5/3