If `lim_(x->oo)((x^2+x+1)/(x+1)-a x-b)=4,t h e n` (a)`a=1,b=4` (b) `a=1,b=-4` (c)`a=2,b=-3` (d) `a=2,b=3`

("lim")_(x->oo){(x^3+1)/(x^2+1)-(a x+b)}=2,t h e n (a) a=1,b=1 (b) a=1,b=2 (c) a=1,b=-2 (d) none of these

If ("lim")_(xto1^-)(2-x+a[x-1]+b[1+x]) exists, then aa n db can take the values of (where [.] denotes the greatest integer function). (a) a=1/3,b=1 (b) a=1, b=-1 (c) a=9, b=-9 (d) a=2, b=2/3

lim_(x->oo)((2x+1)^(40)(4x-1)^5)/((2x+3)^(45)) is equal to (a)16 (b) 24 (c) 32 (d) 8

lim_(x->oo) (e^(1/x^2)-1)/(2tan^-1(x^2)-pi) is equal to (a) 1 (b) -1 (c) 1/2 (d) -1/2

If (lim)_(xvec0)(a e^x+bcos x+c e^(-x))/(e^(2x)-2e^x=1)=4,t h e n a=2 b. b=-4 c. c=2 d. a+b+c=-8

lim_(xvecoo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 (b) oo (c) 1/2 (d) none of these

Let f(x)={(x-4)/(|x-4|)+a ,x 4 Then f(x) is continous at x=4 when a=0,b=0 b. a=1,b=1 c. a=-1,b=1 d. a=-1,b=-1

If ("lim")_(xvec1)(asin(x-1)+bcos(x-1)+4)/(x^2-1)=-2,t h e n|a+b| is_______

lim_(x -> oo)(x(log(x)^3)/(1+x+x^2) equals 0 (b) -1 (c) 1 (d) none of these

("lim")_(xvecoo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) 0 (b) 1 (c) 1/3 (d) 1/2