y=xsin(1/x)的水平渐近线与铅直渐近线?怎么求?

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y=xsin(1/x)的水平渐近线与铅直渐近线?怎么求?
y=xsin(1/x)的水平渐近线与铅直渐近线?怎么求?

y=xsin(1/x)的水平渐近线与铅直渐近线?怎么求?
答:
y=xsin(1/x)水平渐近线求x趋于无穷时极限
y=lim(x→∞) xsin(1/x)
=lim(x→∞) sin(1/x)/(1/x)
=lim(t→0) sint/t
=1
所:y=xsin(1/x)水平渐近线y=1