Find `lim_(x->oo) (2^x-1)/(2^x+1)`

lim_(x->oo) xsin(2/x)

lim_(x->oo)2^xsin(a/2^x)

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):}

If lim_(x->oo) f(x) exists and is finite and nonzero and if lim_(x->oo) {f(x)+(3f(x)−1)/(f^2(x))}=3 ,then the value of lim_(x->oo) f(x) is

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

Solve: lim {x->oo} 2^(x-1) tan(a/(2^x))

lim_(x->oo)(x^2 - sinx)/(x^2-2)

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

Find the value of lim_(x->oo)(2-1/x+4/x^2)