求极限.sin(1-x)/lnx(x趁于1）；(x^2+2x)/sinx(x趁于0）.用等价无穷小代换法求._数学解答

求极限.sin(1-x)/lnx(x趁于1）；(x^2+2x)/sinx(x趁于0）.用等价无穷小代换法求.

人气：491 ℃　时间：2020-02-05 19:23:59

解答

x->1x-1-->0sin(1-x)~1-x
lnx=ln(1+(x-1))~(x-1)
limsin(1-x)/lnx=-1
x->0sinx~x
lim(x²+2x)/sinx=lim(x²+2x)/x=2