If `f(x)=x((e^(|x|+[x])-2)/(|x|+[x]))` then (where [.] represents the greatest integer function) `(lim)_(xvec0^+)f(x)=-1` b. `(lim)_(xvec0^-)f(x)=0` c. `(lim)_(xvec0^)f(x)=-1` d. `(lim)_(xvec0^)f(x)=0`

Evaluate: ("lim")_(xvec0)(tanx)/x where [dot] represents the greatest integer function

Given ("lim")_(xvec0)(f(x))/(x^2)=2, \where\ [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

Evaluate: ("lim")_(xvec0)(sinx)/x,w h e r e[dot] represents the greatest integer function.

Let f(x) = x(-1)^([1//x]); x != 0 where [.] denotes greatest integer function, then lim_(x rarr 0) f (x) is :

Given a real-valued function f such that f(x)={(tan^2{x})/((x^2-[x]^2) sqrt({x}cot{x}),for x 0 Where [x] is the integral part and {x} is the fractional part of x , then ("lim")_(xvec0^+)f(x)=1 , ("lim")_(xvec0^-)f(x)=cot1 , cot^(-1)(("lim")_(xvec0^-)f(x))^2=1 , tan^(-1)(("lim")_(xvec0^+)f(x))=pi/4

Which of the following is and determinate form (lim)_(xvec1)(x^3-1)/(x-1) b. (lim)_(xvec0)(1+x)^(1//x) c. (lim)_(xvec1)(1/(x^2-1)-1/(x-1)) d. (lim)_(xvec0)(|x|)^(s in R)

If f(x)=(3x^2+a x+a+1)/(x^2+x-2), then which of the following can be correct (a) ("lim")_(xvec 1)f(x) for a=-2 (b) ("lim")_(xvec-2)f(x) for a=13 (c) ("lim")_(xvec 1)f(x)=4/3 (d) ("lim")_(xvec-2)f(x)=-1/3

If f(x) = { sin[x]/([x]),[x] != 0 ; 0, [x] = 0} , Where[.] denotes the greatest integer function, then lim_(x rarr 0) f(x) is equal to

Let f(x)=(x^2-9x+20)/(x-[x]) (where [x] is the greatest integer not greater than xdot Then (A) ("lim")_(x->5)f(x)=1 (B) ("lim")_(x->5)f(x)=0 (C) ("lim")_(x->5)f(x) does not exist. (D)none of these

If f(x)={x+1/2, x<0 2x+3/4,x >=0 , then [(lim)_(x->0)f(x)]= (where [.] denotes the greatest integer function)