Let `lim_(x->0)([x]^2)/(x^2)=l and lim_(x->0)([x^2])/(x^2)=m ,` where `[dot]` denotes greatest integer. Then (a)`l` exists but `m` does not (b)`m` exists but `l` does not (c)both l and m exist (d) neither `lnorm` exists

Let Lim_(x rarr1)([x])/(x)=l and lim_(x rarr1)(x)/([x])=m where [ .] denotes the greatest integer function, then

let l=lim_(x rarr2)([x])/({x}) and m=lim_(x rarr2)({x})/([x])

Consider the function f(x) =[(1-x,0 leq x leq 1),(x+ 2, 1 lt x lt 2),(4-x,2 leqxleq4)). Let lim_(x->1) f(f(x))= l and lim_(x->1) f(f(x))=m then which one of the following hold good ? (A) l exist but m does not (B) m exist but l does not (C) both exist (D) both does not exist

If l=lim_(xto1^(+))2^(-2^(1/(1-x))) and m=lim_(xto1^(+))(x sin (x-[x]))/(x-1) (where [.] denotes greatest integer function). Then (l+m) is ………….

The value of lim_(x rarr0)x^(2)[(1)/(x^(2))] where [.] denotes G.L.F.is

If A=lim_(x->0)sin^(-1)(sinx)/(cos^(-1)(cosx)) and B=lim_(x->0)[|x|]/x then (where [.] denotes greatest integer function)(A) A=1 (B) A does not exist (C) B = 0 (D) B=1

lim_(x rarr0)[min(y^(2)-4y+11)(sin x)/(x)](where[.] denotes the greatest integer function is 5(b)6(c)7(d) does not exist

lim_(x->0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot] represents the greatest integer function). (a)-1 (b) 1 (c) 0 (d) does not exist

lim_(xtoc)f(x) does not exist when where [.] and {.} denotes greatest integer and fractional part of x

(lim)_(xvec-7)([x]^2+15[x]+56)/("sin"(x+7)"sin"(x+8))= (where [.] denotes the greatest integer function) a. is 0 b. is 1 c. is -1 d. does not exist