求:lim(x趋向0)∫(0到x)sintdt/∫(0到x)tdt的极限,

问题描述:

求:lim(x趋向0)∫(0到x)sintdt/∫(0到x)tdt的极限,

设(cos0-cosx)/(x^/2)=a原式=lim(x趋向0)(cos0-cosx)/[(x^/2)-0]=a=lim(x趋向0)(1-cosx)/(x^/2)=d[(1-cosx)/x]/dx (x趋向0)=sinx/x-(1-cosx)/(x^/2) (x趋向0)=1-(1-cosx)/(x^/2) (x趋向0)=1-a所以a=1-aa=1/2所以lim(...