Evaluate: `("lim")_(xvecoo)x^(1/x)`

Evaluate lim_(xtooo) x^((1)/(x)).

Evaluate: ("Lim")_(x->0)(1/x)^(tanx)

Evaluate lim_(xtooo) [x(a^(1//x)-1)],agt1

Evaluate: ("Lim")_(x->1)(x^x-x)/(x-1-lnx)

Evaluate: lim_(x rarr oo)[x(a^((1)/(x))-1)],a>1

Evaluate lim_(xto0) (e-(1+x)^(1//x))/(x) .

Evaluate: (lim)_(x rarr oo)(1+(1)/(x))^(x)

The value of (lim)_(xvecoo)[tan^(-1)(x+1)/(x+2)-dotpi/4],w h e r e[x] denotes greatest integer lt=x , is 1/2 b. -1/2 c.1 d. -1

Evaluate lim_(xtooo)(1+2/x)^(x)

Evaluate "lim_(x rarr0)x tan(1/x)