`lim_(x->0) (tanx/x)^(1/x^2)`

Evaluate : lim_(x rarr 0)(tanx/x)^(1/x)

lim_(xrarr0) (tanx-x)/(x^(2)tanx) =?

Let f:(-pi/2, pi/2)->R, f(x) ={lim_(n->oo) ((tanx)^(2n)+x^2)/(sin^2x+(tanx)^(2n)) x in 0 , n in N; 1 if x=0 which of the following holds good?

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

lim_(xrarr0)(tanx-x)/(x^2tanx) equals

Evaluate : lim_( x -> 0 ) ( tanx - x ) / ( x - sinx )

lim_(xrarr0)(tanx-sinx)/(x^3)=

Statement -1: lim_(xrarr pi//2 ) (cot x-cosx)/(2x-pi^3)=(1)/(16) statement 2 lim_(xrarr0) (tanx-sinx)/(x^3)=(1)/(2)

The value of lim_(x->0)((sinx-tanx)^2-(1-cos2x)^4+x^5)/(7(tan^(- 1)x)^7+(sin^(- 1)x)^6+3sin^5x) equal to :