lim(x趋向0)[ln(a+x)+ln(a-x)-2lna]/x^2怎么解?

Question

lim(x趋向0)[ln(a+x)+ln(a-x)-2lna]/x^2怎么解?

Answer 1

应用罗比达法则,分子分母同时求导
lim(x趋向0)[ln(a+x)+ln(a-x)-2lna]/x^2=lim(x趋向0)[1/(a+x)-1/(a-x)]/2x
=lim(x趋向0)-1/(a^2-x^2)=-1/a^2