`lim_(x->oo)((2x-1)/(2x+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):}

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_(x->oo) (2x - 1)/(x + 2)

lim_(x rarr oo) ((x-1)(2x-1))/((x-4)(x-7))= _____.

Solve: lim_(x->oo)2^(x-1) tan(a/(2^x))

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

lim_(x->oo) (x-sqrt(x^2-1))

Evaluate: lim_(x rarr oo)[(x-1)/(x-2)]^x

lim_(x rarr oo)((x)/(1+x))^((x)/(2))=