求极限 lim(xsin2/x+sin3x/x) x趋向于无穷

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求极限lim(xsin2/x+sin3x/x)x趋向于无穷求极限lim(xsin2/x+sin3x/x)x趋向于无穷求极限lim(xsin2/x+sin3x/x)x趋向于无穷lim(xsin2/x+s

求极限 lim(xsin2/x+sin3x/x) x趋向于无穷
求极限 lim(xsin2/x+sin3x/x) x趋向于无穷

求极限 lim(xsin2/x+sin3x/x) x趋向于无穷
lim(xsin2/x+sin3x/x) = lim(xsin2/x)+limsin3x/x
x趋向无穷大2/x趋向于0,使用等价无穷小替换lim(xsin2/x)=2,又因为sin3x有界而x为无穷大,有界/无穷大=0,所以
lim(xsin2/x+sin3x/x) =2

lim(xsin2/x+sin3x/x)
=lim2sin(2/x)/(2/x)+limsin3x/x
=2+0=2