lim x—∞[ (x+1)/(x平方+1) ] - 知识问答

lim x—∞[ (x+1)/(x平方+1) ] arctanx

2个回答

lim（x→+∞) [ (x+1)/(x²+1) ] arctanx
=lim（tan x→+∞) [ (tan x + 1)/(tan²x+1) ] arctan(tan x)
=lim(x→π/2) [sin x ·cos x + cos²x]·x
=lim(x→π/2) cos x(sin x + cos x)·x
=0·1·π/2
=0

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