求lim(x趋近于π)(π-x)tan(x/2)的极限?

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求lim(x趋近于π)(π-x)tan(x/2)的极限?

求lim(x趋近于π)(π-x)tan(x/2)的极限?
求lim(x趋近于π)(π-x)tan(x/2)的极限?

求lim(x趋近于π)(π-x)tan(x/2)的极限?
π-x 趋近于0;
tan(x/2)趋近于∞;
lim(x趋近于π)(π-x)tan(x/2)
=lim(x趋近于π)(π-x)/ (cos(x/2)/sin(x/2))
=(分子分母同时求导)lim(x趋近于π)2*(-1)/(-1/(sin x/2)^2 )
=lim(x趋近于π)(-2)*(sin π2)^2 / (-1) =2 .