高等数学试题

=lim(x→0)[(cotx)^2-x^2]/x^2(cotx)^2

=lim(x→0)[(cosx)^2-x^2sinx^2]/[x^2cosx^2]

=lim(x→0)[-x^2+(1+x^2)cosx^2]/[x^2cosx^2]

=+∞

lim(x→1)(1-x)(tan(πx/2)

= lim(x→1)(1-x)/cot(πx/2)

= lim(x→1)(1-x)'/cot(πx/2)'

= lim(x→1)(-1)/[(π/2)/-(sinπx/2)^2)

=2/π