If `f(x)=|x-1|-[x],w h e r e[x]` is the greatest integer less then or equal to `x` , then a. `f(1+0)-1,f(1-0)=0` b. `f(1+0)=0=f(1-0)` c. `("lim")_(xvec1)f(x)e xi s t s` d. `("lim")_(xvec1)f(x)doe snote xi s t`

Evaluate: ("lim")_(xvec0)(1+x)^(os e cx c)

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

If f(x)={(x-|x|)/x ,x!=0 ,x=0,s howt h a t("lim")_(xto0) f(x) does not exist.

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")_(xvec1)(x^2+x(log)_e x-(log)_e x-1)/((x^2-1)

f(x)={x ,xlt=0 1,x=0,then find ("lim")_(xvec0) f(x) if exists x^2,x >0

If f(x)=x(-1)^[1/x] xle0 , then the value of lim_(xto0)f(x) is equal to

("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

If f(x)={[x]+sqrt({x}),x<1 1/([x]+{x}^2),xgeq1 , then [where [.] and {.] represent the greatest integer and fractional part functions respectively] f(x) is continuous at x=1 f(x) is not continuous at x=1 f(x) is differentiable at x=1 (lim)_(xvec1)f(x) does not exist