`lim_(x to oo) (3^x-1)/(4^x-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):}

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

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

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

Evaluate the following limits : lim_(x to oo) (2x^(2)+7x+5)/(4x^(2)+3x-1)

(i) underset(x to oo)(Lt) e^(x) "sin" (Ke^(-x)) (ii) lim_(x to oo) (("sin"(3)/(4^(x)))/(tan (4)/(3^(x)))) (iii) lim_(x to oo) (1 - a^(4))^(-x) tan( b (1 - a^(4))^(x)) , -1 lt a lt 1, a != 0 and b in R

Evaluate : lim_(x to oo) ((x-3)/(x+3))^(x+3)

If lim_(x to 1) (x^(3) - 1)/(x - 1) = lim_(x to k) (x^(4) - k^(4))/(x^(3) - k^(3)) , find the value of k.

The value of lim_(x to oo)((1+3x)/(2+3x))^((1-sqrt(x))/(1-x)) is

Evaluate the following limits : Lim_(x to oo) ((x+6)/(x+1))^(x+4)