lim(sin2t+cost)的T分之一次方 t-->o

Question

lim(sin2t+cost)的T分之一次方 t-->o

Answer 1

这道挺棘手的,先用洛必达法则好了
lim[t→0] (sin2t+cost)^(1/t)
=e^lim[t→0] ln(sin2t+cost)^(1/t)
=e^lim[t→0] ln(sin2t+cost)/t
=e^lim[t→0] (2cos2t-sint)/(sin2t+cost)
=e^2lim[t→0] (cos2t-sint)/(sin2t+cost)
=e^2*(1-0)/(0+1)
=e²