求极限
lim(x趋于∞) 【(3x^2+5)/(5x+3)】×sin2/x
lim(x趋于∞) 【(3x^2+5)/(5x+3)】×sin2/x lim[(3x^2+5)/(5x+3)]*sin(2/x) 令t=1/x,则x→∞时,t→0 那么,原式=lim[(3/t^2+5)/(5/t+3)]*sin2t =lim[(5t^2+3)/(3t^2+5t)]*2sintcost =lim[(5t^2+3)/(3t^2+5t)]*2sint*1 =lim(5t^2+3)*[2/(3t+5)]*[(sint)/t] =lim[(5t^2+3)*2]/(3t+5)*1 =6/5
问:求极限limX趋向于π时: 求[√(1-tanX)-√(1+tanX)]/sin2X的极限?
答:解:lim[√(1-tanx)-√(1+tanx)]/sin2x(分子有理化) =lim[(1-tanx)-(1+tanx)]/{sin2x[√(1-tanx)...详情>>
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