`lim_(x to -oo) 2^x`

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

lim_(x to oo) ((x^(2)+ 5x+3)/(x^(2)+x+3))^(x) is equal to

Evaluate the following limits : lim_(x to oo) (2 sin x - sin 2 x)/(x^(3))

The value of lim_(x to oo ) (x-x^(2)log_(e)(1+(1)/(x))) is _______.

f (x) = lim _(x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +1),n in N and g (x) =tan ((1)/(2)sin ^(-1)((2f (x))/(1+f ^(2) (x)))), then lim_(x to -3) ((x ^(2) +4x +3))/(sin (x+3) g (x)) is equal to:

{:("Column-I","Column-II"),(A.lim_(x to 0) (cos x - cos3x)/(x("Sin"x - "sin"3x)),p. 3),(B.lim_(x to 0) ("sin" 4x)/(tan 2x),q. -2),(C. lim_(x to oo) (x^(4) + 2x^(3) + 3)/(2x^(4) - x + 2),r.(1)/(2)),(D.lim_(x to 2) (sqrt(3x^(2) + 3x - 9) - sqrt(3x + 3))/(x - 2),s. 2):}

Evaluate lim_(x to oo) (sinx^(0))/(x).

Evaluate the following limits : Lim_(x to oo) ((x+1)(2x+3))/((x+2)(3x+4))