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`

lim_(xto0) [(1-e^(x))(sinx)/(|x|)] is (where [.] represents the greatest integer function )

f:(2,3)->(0,1) defined by f(x)=x-[x] ,where [dot] represents the greatest integer function.

Evaluate : [lim_(x to 0) (tan x)/(x)] , where [*] represents the greatest integer function.

Evaluate : [lim_(x to 0) (sin x)/(x)] , where [*] represents the greatest integer function.

Evaluate: [("lim")_(xrarr0)(tan^(-1)x)/x], where [.]represent the greatest integer function

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

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

The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (where [.] represents the greatest integer function). -1 (b) 1 (c) 0 (d) none of these

The function f(x) =p [x+1] +q [x-1] where [x] is the greatest integer function, and lim _(xto1+) f(x) =lim _(x to 1-) f(x)= f(1) when-

Which of the following true ({.} denotes the fractional part of the function)? ("lim")_(xvecoo)((log)_e x)/({x})=oo (b) ("lim")_(xvec2^+)x/(x^2-x-2)=oo ("lim")_(xvec1^-)x/(x^2-x-2)=-oo (d) ("lim")_(xvecoo)((log)_(0.5) x)/({x})=oo