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

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

lim_(x->oo)(1-x+x.e^(1/n))^n

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

lim_(n rarr oo)2^(1/n)

lim_(n->oo)2^(n-1)sin(a/2^n)

If A=[{:(,1,a),(,0,1):}] then find lim_(n-oo) (1)/(n)A^(n)

Given that lim_(nto oo) sum_(r=1)^(n) (log (r+n)-log n)/(n)=2(log 2-(1)/(2)) , lim_(n to oo) [(1)/(n^k)[(n+1)^k(n+2)^k.....(n+n)^k]]^(1//n) , is

Prove that lim_(xrarr0) ((1+x)^(n) - 1)/(x) = n .

If the value of lim_(n->oo){1/(n+1)+1/(n+2)+.......+1/(6n)} is 'K' then find value of (K - log_e 6)? .

The value of lim_(n->oo) sum_(k=1)^n log(1+k/n)^(1/n) ,is