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

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

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

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^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

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

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)

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)