4.解：lim(x->0)[sin(3x)/sin(5x)]
=lim(x->0)[(3/5)*(sin(3x)/(3x))*(sin(5x)/(5x))]
=(3/5)*lim(x->0)[sin(3x)/(3x)]*lim(x->0)[sin(5x)/(5x)]
=(3/5)*1*1 (应用重要极限lim(z->0)(sinz/z)=1)
=3/5。
lim(n->∞)[2^n*sin(x/2^n)]
=lim(n->∞)[x*sin(x/2^n)/(x/2^n)]
=x*lim(n->∞)[sin(x/2^n)/(x/2^n)]
=x*1 (应用重要极限lim(z->0)(sinz/z)=1)
=x。
3/5等价代换
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024