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

If L=+(lim)_(x->1)((2x-3)(sqrt(x)-1))/(2x^2+x-3),\ t h e n\ 20\ L=

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")_(xvec1)((7-x)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_(x->1)((x^n-1)/(n(x-1)))^(1/(x-1))=e^p , then p is equal to

lim_(x->0)(e^(x)-1)/(sqrt(4+x)-2) =

If (lim)_(xvec0)(x^3)/(sqrt(a+x)(b x-sinx))=1,a >0t h e na+b is equal to a. 36 b. 37 c. 38 d. 40

The value of (lim)_(xvecoo)[tan^(-1)(x+1)/(x+2)-dotpi/4],w h e r e[x] denotes greatest integer lt=x , is 1/2 b. -1/2 c.1 d. -1

lim_(xrarr0) (ax-(e^(4x)-1))/(ax(e^(4x)-1)) = b .Find a-2b

Which of the following limits tends to unity? (a) ("lim")_(xvec0)sin(tanx)/(sinx) (b) ("lim")_(xvecpi/2)sin(cosx)/(cosx) ("lim")_(xvec0)"sin"(e^x-1)/x (d) ("lim")_(xvec0)(sqrt(1+x)-sqrt(1-x))/x