求助,哪位数学学霸教我一下,第三题

2025-05-21 16:47:18
推荐回答(1个)
回答(1):

ln2+ln3
解析:
(x→0)lim(2^x+3^x-1)/(kx)=1
故,
(x→0)lim(2^x+3^x-1)/(kx)
=(x→0)lim(2^x+3^x-1)'/(kx)'
=(x→0)lim(2^xln2+3^xln3)/k
=(ln2+ln3)/k
=1
所以,k=ln2+ln3