Question

(cos2x)的1+cotx&sup2次方的极限,当x趋向于0时.

Answer 1

lim(x→0) (cos2x)^(1+(cotx)^2)

=lim(x→0) (cos2x)^(1/(sinx)^2)

=lim(x→0) (1-2(sinx)^2)^(1/(sinx)^2)

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

=e^(-2)