Question

如图。该极限怎么求？

求详细步骤。用洛必达法则可以吗？

Answer 1

x->0
√(1-x^2) = 1- (1/2)x^2 +o(x^2)
1-√(1-x^2) = (1/2)x^2 +o(x^2)
lim(x->0) x^2/[1-√(1-x^2)]
=lim(x->0) x^2/[(1/2)x^2)]
=2