x→0时cos1/x的极限

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x→0时cos1/x的极限x→0时cos1/x的极限x→0时cos1/x的极限不存在.是无限震荡的,不会趋于一个定值,故极限不存在.doesn''texist.proof:considerXn=1/(n

x→0时cos1/x的极限
x→0时cos1/x的极限

x→0时cos1/x的极限
不存在.
是无限震荡的,不会趋于一个定值,故极限不存在.

doesn't exist.
proof:
consider Xn=1/(npi) n is in natural number
Xn doesn't equal to 0
lim Xn=0
and f(Xn)=cos(1/(1/npi))=cos(npi)=(-1)^n
which is not a convergent sequence.
so the limit doesn't exist.