求当x趋于1时sin^2(1-x)/(x-1)^2(x+2)的极限没有就不要写了

Question

求当x趋于1时 sin^2(1-x)/(x-1)^2(x+2)的极限 没有就不要写了

Answer 1

(x→1) lim sin^2(1-x) / [(x-1)^2(x+2)]
=(x→1) lim sin^2(1-x) / (1-x)^2 / (x→1)lim (x+2)
=(x→1) lim [sin(1-x) / (1-x)]^2 / 3
=[(x→1) lim sin(1-x) / (1-x)]^2 / 3 利用重要极限 (x→0) lim (sinx)/x =1
=1^2/3
=1/3