5) `lim_(x->oo) ((x+1)/(x-1))^x = e^2`

lim_(x->e) (lnx-1)/(x-e)

lim_(x->oo)sin(1/x)/(1/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):}

lim_(xto oo)(x/(1+x))^(x) is

lim_(x->oo) ((x^2-2x+1)/(x^2-4x+2))^x is equal to

lim_(xrarr oo) ((x+5)/(x-1))^(x) is equal to

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

lim_(x->oo)(1-x+x.e^(1/n))^n

lim_(xrarr oo) (1+(2)/(x))^x equals

lim_(x->oo)(e^(11x)-7x)^(1/(3x))