作业帮求:lim(x趋向0)∫(0到x)sintdt/∫(0到x)tdt的极限,
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求:lim(x趋向0)∫(0到x)sintdt/∫(0到x)tdt的极限,
求:lim(x趋向0)∫(0到x)sintdt/∫(0到x)tdt的极限,
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-a
a=1/2
所以lim(x趋向0)∫(0到x)sintdt/∫(0到x)tdt的极限为1/2
原式属于0/0型极限,可用洛泌塔法则
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