`lim_(n->00)0=`

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|

If f(x) = lim_(n->oo) tan^(-1) (4n^2(1-cos(x/n))) and g(x) = lim_(n->oo) n^2/2 ln cos(2x/n) then lim_(x->0) (e^(-2g(x)) -e^(f(x)))/(x^6) equals

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

If n is a non zero integer and [*] denotes the greatest integer function then lim_(x->0)[nsinx/x] + lim_(x->0)[ntanx/x] equals

lim_(x->0)((1^x+2^x+3^x+....+n^x)/n)^(1/x)

Evaluate: lim_(x->0)x^m(logx)^n ,m , n in Ndot

lim_(x->0)((1^x+2^x+...........+n^x)/n)^(1/x) is equal to

If and n are positive integers, then lim_(x->0)((cosx)^(1/ m)-(cosx)^(1/ n))/(x^2) equal to :

The integer n for which lim_(x->0)((cosx-1)(cosx-e^x))/(x^n) is finite nonzero number is ________

The integer n for which lim_(x->0)((cosx-1)(cosx-e^x))/(x^n) is finite nonzero number is ________