`(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)\ `

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 rarr oo)(x)/(e^(x))=?

(lim)_(x->0)((1-t a n x)/(1+sin x))^(cos e c\ x)

lim_(x rarr oo)(1+e^(-x))^(e^(x))=

("lim")_(xvec1)[cos e c(pix)/2]^(1/((1-x)))(w h e r e[dot]r e p r e s e n t st h e gif is e q u a l to (a) 0 (b) 1 (c) oo (d) does not exist

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

lim_ (x rarr oo) (x ^ (n)) / (e ^ (x)) = 0, (n is an integer) for

lim_(x rarr oo)(1-x+x*e^((1)/(n)))^(n)

sum_(n=0)^(oo)((log_(e)x)^(n))/(n!) is equal to