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 l nor m` exists

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->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")_(xvec1)(xsin(x-[x]))/(x-1),w h e r e[dot] denotes the greatest integer function is equal to (a) 0 (b) -1 (c) not exist (d) none of these

("lim")_(xvec0)[(sin(sgn(x)))/((sgn(x)))], where [dot] denotes the greatest integer function, is equal to (a)0 (b) 1 (c) -1 (d) does not exist

If [dot] denotes the greatest integer function, then (lim)_(xvec0)x/a[b/x] b/a b. 0 c. a/b d. does not exist

lim x→(2^+) { x } sin( x−2 ) /( x−2)^2 = (where [.] denotes the fractional part function) a. 0 b. 2 c. 1 d. does not exist

Given ("lim")_(xvec0)(f(x))/(x^2)=2,w h e r e[dot] denotes the greatest integer function, then (a) ("lim")_(xvec0)[f(x)]=0 (b) ("lim")_(xvec0)[f(x)]=1 (c) ("lim")_(xvec0)[(f(x))/x] does not exist (d) ("lim")_(xvec0)[(f(x))/x] exists

Let f(x)=(x^2-9x+20)/(x-[x]) (where [x] is the greatest integer not greater than xdot Then (a) ("lim")_(xvec5)f(x)=1 (b) ("lim")_(xvec5)f(x)=0 (c) ("lim")_(xvec5)f(x)does not exist (d)none of these

Let f(x)={{:(cos[x]", "xle0),(|x|+a", "xlt0):}. Then find the value of a, so that lim_(xto0) f(x) exists, where [x] denotes the greatest integer function less than or equal to x.