`L i m i t\ l=(lim)_(x->oo)(pi/2-t a n^-1\ x)/(ln(1-1/x))` equals

lim_ (x rarr oo) {xx ^ (2) ln (1+ (1) / (x))}

L=lim_(x rarr oo)((log x)/(x))^((1)/(x))

lim_(x->oo)x(a r c t a n(x+1)/(x+2)-a r c t a n x/(x+2)) is equal to

lim_(x rarr oo)((1+x+x^(2)))/((ln x)^(3)) is equal to

The value of limit lim_(x rarr oo)pi(x ln(1+pi x)-x ln(pi x)) is

The value of lim_(x to - pi) (int_(0)^(sin x)sin^(-1)t dt)/((x+pi)^(2)) is equal to L then find the value of 100 L :

lim_ (x rarr oo) {xx ^ (2) * log (1+ (1) / (x))}

If I_(n)=int_(0)^(pi//4) tan^(n) x dx, lim_(n to oo) n(I_(n+1)+I_(n-1)) equals

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