Question

求问第二小题怎么做！求详细步骤！

求问第二小题怎么做！求详细步骤！高数内容！谢谢

Answer 1

A=max{ a1,a2,...,am }
consider
L = lim(x->∞) [ (a1)^x +(a2)^x +...+(am)^x ]^(1/x)
lnL
= lim(x->∞) ln[ (a1)^x +(a2)^x +...+(am)^x ] /x (∞/∞)
= lim(x->∞) { (lna1)(a1)^x +(lna2)(a2)^x +...+(lnam)(am)^x }
/ [ (a1)^x +(a2)^x +...+(am)^x ]
= lim(x->∞) { (lna1)(a1/A)^x +(lna2)(a2/A)^x +...+(lnam)(am/A)^x }
/ [ (a1/A)^x +(a2/A)^x +...+(am/A)^x ]
= lnA
=> L = A
=>lim(n->∞) [ (a1)^n +(a2)^n +...+(am)^n ]^(1/n) = A

Answer 2

68.四个头——天上有日