x趋近于无穷 1/sinx 的极限为多少 是零吗?
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limsinx\uff08x->0\uff09=0
limx\uff08x->0\uff09=0
\uff08sinx\uff09'=cosx\uff1b(x)'=1
=lim(sinx/x)
=lim(cosx/1)
=cos0
=1
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lim(x->∞) 1/sin x = 极限不存在(sin x 不趋于确定的值)!
lim(x->∞) sin(1/x) =sin(0) = 0
lim(x->∞) (sinx)/x = 0
lim(x->0) (sinx)/x = 1
是发散的,在1到无穷大之间剧烈震荡。sin(1/x)的极限才是0
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