Question

一题微积分求极限.希望过程清楚点,

Answer 1

lim[(2-x)/2]^(2/x)

=lim[1-x/2]^(2/x) 设 t = -x/2,则当 x →0 时 t →0

=lim(1+t)^(-1/t) 注：此时极限变成当 t →0

=lim[(1+t)^(1/t)]^(-1)

=[lim(1+t)^(1/t)]^(-1)

=e^(-1)

=1/e