Question

求极限 lim(x→∞)(1-kx)∧(1/x),

Answer 1

利用极限

lim x->无穷 (1-x)^(1/x)=1/e

lim(x→∞)(1-kx)∧(1/x)

=lim(x→∞)[(1-kx)∧(1/(kx))]^k

=[lim(x→∞)(1-kx)∧(1/(kx))]^k

=[e^(-1)]^k

=e^(-k)