Question

用洛必达法则求下列各极限Limx→(π/2)+ ln(x-π/2)/tanx limx→+∞x∧n/e∧ax,a>0,n

Answer 1

这怎么会是难题呢？依样画葫芦即可：

lim(x→π/2+)ln(x-π/2)/tanx (∞/∞)

= lim(x→π/2+)[1/(x-π/2)]/sec²x

= lim(x→π/2+)[cos²x/(x-π/2)] (0/0)

= lim(x→π/2+)[2cosx(-sinx)/1]

= 0。