x→∞lim(x-cosx)/x=?
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x→∞lim(x-cosx)/x=?
x→∞lim(x-cosx)/x=?
x→∞lim(x-cosx)/x=?
∵lim(x→∞)[(x-cosx)/x]=lim(x→∞)(1-cosx/x)=1-lim(x→∞)(cosx/x).
显然,cosx是有界的,∴lim(x→∞)(cosx/x)=0,∴lim(x→∞)[(x-cosx)/x]=1.
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