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

If lim_(xto1)(asin(x-1)+bcos(x-1)+4)/(x^(2)-1)=-2 , then |a+b| is__________.

If lim_(xrarr1)((asin(x-1)+bcos(x-1)+4))/(x^2-1)=2 , then (a,b) is equal to

Evaluate: ("lim")_(xvec0)1/xsin^(-1)((2x)/(1+x^2))

Each question contains statements given in two columns which have to be matched. Statements a,b,c,d in column I have to be matched with statements p,q,r,s in column II. If the correct match are a-p, a-s, b-r, c-p, c-q, and d-s, then the correctly bubbled 4 x 4 matrix should be as follows: fig Column I, Column II If L=""("lim")_(xvec-1)((7-x)^(1/3)-2)/((x+1)),t h e n12 L= , p. -2 If L=""("lim")_(xvecpi/4)(tan^3x-tanx)/(cos(x+pi/4)),t h e n-L/4= , q. 2 If L=""("lim")_(xvec1)((2x-3)(sqrt(x)-1))/(2x^2+x-3),t h e n20 L= , r. 1 If L=""("lim")_(xvecoo)(logx^n-[x])/([x]),w h e r en in N ,([x] denotes greatest integer less than or equal to x),t h e n-2L= , s. -1

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

Evaluate : ("lim")_(xvec1)(2/(1-x^2)+1/(x-1))

("lim")_(xvec1)(1-x)tan(pix)/2=_____

Evaluate: ("lim")_(xvec2)(x-2)/((log)_a(x-1))

Let ("lim")_(xvec1)(x^a-a x+a-1)/((x-1)^2)=f(a)dot Then the value of f(4) is _________

Evaluate: ("lim")_(xvec0) ((1+x)^(1/x)-e+1/2e x)/(x^2)