分类：教育/科学-理工学科-数学
问题：求极限lim(x趋于∞)【(3x^2+5)/(5x+3)】×si 
lim(x趋于∞)  【(3x^2+5)/(5x+3)】×sin2/x
回答：lim(x趋于∞) 【(3x^2+5)/(5x+3)】×sin2/x

lim<x→∞>[(3x^2+5)/(5x+3)]*sin(2/x)
令t=1/x，则x→∞时，t→0
那么，原式=lim<t→0>[(3/t^2+5)/(5/t+3)]*sin2t
=lim<t→0>[(5t^2+3)/(3t^2+5t)]*2sintcost
=lim<t→0>[(5t^2+3)/(3t^2+5t)]*2sint*1
=lim<t→0>(5t^2+3)*[2/(3t+5)]*[(sint)/t]
=lim<t→0>[(5t^2+3)*2]/(3t+5)*1
=6/5