c=[c^n]^(1/n)≤[a^n+b^n+c^n]^(1/n] ≤[3*c^n]^(1/n)=c*3^(1/n]
lim[n—& gt；∞] 3^(1/n) =1
∴lim[n—>∞][a^n+b^n+c^n]^(1/n]= c
Cuando 0≤x≤1, 2x ≤ 2, x 2 ≤ 2.
∴lim[n—>∞][2^n+(2x)^n+(x^2)^n)]^(1/n] = 2
Cuando 1≤x≤2, 2 ≤ 2x, x 2 ≤ 2x
∴lim[n—>∞][2^n+(2x)^ n+( x^2)^n)]^(1/n)= 2x
Cuando 2≤x, 2x ≤ x 2, 2x ≤ x 2.
∴lim. —>∞][2^n+(2x)^n+(x^2)^n)]^(1/n]=x^2