`lim_(n->oo)(1-1/n^2)^n`

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

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) nsin(1/n)

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

Evaluate the following limit: (lim)_(n->oo)(1/(n^2)+2/(n^2)+3/(n^2)++(n-1)/(n^2\ ))

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

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

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

Evaluate: lim_(n->oo)(-1)^(n-1)sin(pisqrt(n^2+0. 5 n+1)) ,where n in N

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|