lim(x->无穷)n^2(1-cos(1/n))急求解析,

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lim(x->无穷)n^2(1-cos(1/n))急求解析,lim(x->无穷)n^2(1-cos(1/n))急求解析,lim(x->无穷)n^2(1-cos(1/n))急求解析,lim(x→∞)x&

lim(x->无穷)n^2(1-cos(1/n))急求解析,
lim(x->无穷)n^2(1-cos(1/n))急求解析,

lim(x->无穷)n^2(1-cos(1/n))急求解析,
lim(x→∞)x²(1-cos(1/x))
=lim(x→∞)(1-cos(1/x))/(1/x²)
=lim(x→∞)(-sin(1/x)/x²)/(-2/x³)
=lim(x→∞) sin(1/x)/( 2/x)
=lim(x→∞) sin(1/x)/( 1/x)/2
=lim(x→0) (sin(x)/x)/2
=1/2