Question

求极限，，

求极限，，根号二分之一怎么得到的

Answer 1

lim(n->∞) 1/(2n^2+lnn+1)^(1/(2n) ) =1
/
lim(n->∞) n/[ n^(1/n) .(2n^2+lnn+1)^(1/2 )]
=lim(n->∞) n/(2n^2+lnn+1)^(1/2)

=lim(n->∞) 1/(2+lnn/n^2+1/n^2)^(1/2)
=1/√2
/
lim(n->∞) n/ n^(1/n) .(2n^2+lnn+1)^(1/2 ) .lim(n->∞) 1/(2n^2+lnn+1)^(1/(2n) )
=1/√2