Question

当x趋近0时,求(2sinx+cosx-1)/x的极限

Answer 1

(2sinx+cosx-1)/x=[4sin(x/2)cos(x/2)+1-2sin(x/2)sin(x/2)-1]/x=sin(x/2)[sin(x/2)+2cos(x/2)]/(x/2)显然,当x→0,sin(x/2)[sin(x/2)+2cos(x/2)]/(x/2)=sin(x/2)+2cos(x/2)=2.或者因为x→0,(2sinx+cosx-1)/x为0/0型,...