`"I f"f(x)={([tanx])/([x]),[x]!=0 0,[x]=0,"w h e r e"[dot]=G I F ,"t h e n"` `("lim")_(xvec0^-)f(x)=1` (b) `("lim")_(xvec0^+)f(x)=1` `("lim")_(xvec0^+)f(x)=0` (d) `f(0)=0`

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

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)(x2^x-x)/(1-cosx)

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

Evaluate: ("lim")_(xvec0)(2^x-1)/(sqrt(1+x)-1)

Evaluate: ("lim")_(xvec0)(e^x^2-cosx)/(x^2)

Evaluate: ("lim")_(xvec0)(1-cosm x)/(1-cosn x)

Find ("lim")_(xvec0){tan(pi/4+x)}^(1//x)

Evaluate: ("lim")_(xvec0)(tanx-sinx)/(x^3)

Evaluate: ("lim")_(xvec0)(e^x+e^(-x)-2)/(x^2)