`lim_(n->00)n^(1/n)=`

The value of lim_(n->oo) n^(1/n)

lim_(n->oo) nsin(1/n)

7. lim_(n->oo) (2^(1/n)-1)/(2^(1/n)+1)

f'(0) = lim_(n->oo) nf(1/n) and f(0)=0 Using this, find lim_(n->oo)((n+1)(2/pi)cos^(- 1)(1/n)-n)),|cos^(-1)1/n|

Prove that lim_(n->oo)(1+1/n)^n=e

lim_(n->oo)(1/(n^2+1)+2/(n^2+2)+3/(n^2+3)+....n/(n^2+n))

lim_(n->oo)[(1+1/n^2)(1+2^2 /n^2)(1+3^2 /n^2)......(1+n^2 / n^2)]^(1/n)

lim_(n->oo)((n^2-n+1)/(n^2-n-1))^(n(n-1)) is

lim_(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

Evaluate: lim_(n->oo)[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]