Question

求极限：lim(x+e的x次方)2/x次方

Answer 1

lim(x→0) (x+e^x)^(2/x)

= lim(x→0) [1+(x+e^x-1)]^(2/x)

= lim(x→0) [1+(x+e^x-1)]^[1/(x+e^x-1) * (x+e^x-1)*(2/x)] 0) (1+y)^1/y=e,y=x+e^x-1

= e^2lim(x→0) (x+e^x-1)/x

= e^2lim(x→0) [1 + (e^x-1)/x] 0) (e^x-1)/x = 1

= e^[2(1+1)]

= e⁴