Question

高数求极限问题。

求x趋于1时，(cosπx/2)/x^2*(x-1)的极限
要过程。谢谢

Answer 1

lim(x->1) (cosπx/2)/x^2*(x-1)
=lim(x->1) { cos[π(x-1)/2 + π/2)]}/x^2*(x-1)
=lim(x->1) {sin[π(x-1)/2]/(x-1)} *[1/x^2]
=lim(x->1) {[π(x-1)/2]/(x-1)}*[1/x^2]
= π/2 * 1
= π/2