高数-cos√x 求极限问题

Question

这个极限要怎么做，求写一下做题过程

Answer 1

令√x = t， 则x→0时,t→0

原式= lim (cost)^(π/t²)

=lim (1 + (cost-1) )^(π/t²)

=lim (1 + (cost-1) )^(1/(cost-1) * (cost-1)π/t²)

=lim ( (1 + (cost-1) )^(1/(cost-1)) )^ (cost-1)π/t²)

注意到 cost-1与 -t²/2等价

所以原式 = e^(-π/2)本回答被提问者和网友采纳