Question

当x趋近于零时lim(a^x-a^-x)/x=?

Answer 1

等价无穷小代换

当 x->0 时,e^x - 1 x

a^x -1 = e^(lna *x) - 1 (lna) x

lim[(a^x -1 )/x,x->0] = lna

lim[(a^(-x) -1 )/ (-x),x->0] = lna

原式 = lim[ (a^x -1 )/x + [(a^(-x) -1 )/ (-x),x->0] = 2lna