lim(sin3x/x^3+a/x^2)=b (x趋于0) 求a,b
问题描述：
lim(sin3x/x^3+a/x^2)=b (x趋于0) 求a,b
答
lim(x→0)(sin3x/x^3+a/x^2)
=lim(x→0)(sin3x-ax)/x^3 (0/0)
=lim(x→0)(3cos3x-a)/(3x^2)
因为极限存在,所以3cos3x-a＝0
a=3
=lim(x→0)(cos3x-1)/(x^2)
=lim(x→0)[(3x)^2/2]/(x^2)
=9/2=b