x/1乘以sinx+x乘以sinx/1的极限是什么?x趋近于零时
问题描述:
x/1乘以sinx+x乘以sinx/1的极限是什么?x趋近于零时
上面的不对,x分之1乘以sinx+x乘以sinx分之1的极限?当x趋近去零时
答
lim(x→0)[(1/x)sinx+xsin(1/x)]=lim(x→0)[(1/x)sinx]+lim(x→0)[xsin(1/x)]=1+lim(x→0)[xsin(1/x)].∵-1≦sin(1/x)≦1,∴lim(x→0)[xsin(1/x)]=0.∴lim(x→0)[(1/x)sinx+xsin...