`lim_(x to oo) (a^(1/x)-1)x`

Evaluate lim_(x to oo) x("tan"^(-1)(x+1)/(x+4)-(pi)/(4)).

Evaluate the following limit: (lim)_(x->oo)(a^(1//x)-1)x

Find the value of lim _(x to oo) (x+(1)/(x))e ^(1//x)-x.

Match the following : {:("Column-I" , " Column - II"), ("(A)" lim_(x to pi/4)(sin2x)^(tan^(2)2x), "(p)" 1/2),("(B)" lim_(x to oo) ((2x-1)/(2x+1))^(x) , "(q)"e^(-1/2)),("(C)" lim_(x to pi/2)(tanx)^(tan 2x) , "(r)" e^(-1)),("(D)" lim_(x to pi/4) tan2x tan(pi/4-x), "(s)" 1):}

Evaluate: ("lim")_(x->oo)[x(a^(1/x)-1)], a >1

Evaluate the following limits : Lim_(x to oo) ((x-1)/(x+1))^(2)

Evaluate the following limits : Lim_(xto oo) x tan (1/x)

The value of lim_(xto oo)(x+2)tan^(-1)(x+2)-(xtan^(-1)x) is

Evaluate lim_(x to oo ) [sqrt(a^(2)x^(2)+ax+1)-sqrt(a^(2)x^(2)+1)].

Evaluate the following limits : Lim_(x to oo) (3x^(2)+x-1)/(x^(2)-x+7)