If `L=(lim)_(x->oo)(logx^n-[x])/([x]),\ w h e r e\ n in N ,\ t h e n-2L=`

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

(lim)_(x->oo)(logx^n-[x])/([x]),\ n in N ,\ ([x]\ d e not e s\ t h e\ in t ege r\ l e s stanor\ e q u a l\ to\ x)\

lim_(xrarr oo) (logx^n-[x])/([x]) where n in N and [.] denotes the greatest integer function, is

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

x=y ln(xy),t h e n

Evaluate the following limits: (lim)_(x->oo)(1+1/(a+b x))^(c+dx)w h e r e\ a ,\ b ,\ c\ a n d\ d are positive.

Find the value of a for which the following function is continuous at a given point. f(x)={(x^2+3x-10)/(x^2+2x-15),\ w h e n\ x!=-5a ,\ w h e n\ x=-5

The value of lim_(x->oo)((2^(x^n))^(1/e^x)-(3^(x^n))^(1/e^x))/(x^n) (where n in N) is (a)logn(2/3) (b) 0 (c) nlogn(2/3) (d) none of defined

If L=lim_(x rarr oo){x-x^(2)log_(e)(1+(1)/(x))}, then the value of 8L is