lim(x→0)sin5X/sin3X

问题描述:

lim(x→0)sin5X/sin3X

lim(x→0)[ (sin5x/5x)×5x]/[(sin3x/3x)×3x]
=lim(x→0)5x/3x
=5/3

0/0型的极限,x趋近0时,sinx=x
lim(x-->0)sin3x/sin5x
=lim(x-->0)3x/5x
=3/5