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

Let f(x) = (x^2-9x+20)/(x-[x]) where [x] denotes greatest integer less than or equal to x ), then

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

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

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

If ("lim")_(xveca)[f(x)+g(x)]=2a n d ("lim")_(xveca)[f(x)-g(x)]=1, then find the value of ("lim")_(xveca)f(x)g(x)dot

If f(x)=(cosx)/((1-sinx)^(1/3)) then (a) ("lim")_(xrarrpi/2)f(x)=-oo (b) ("lim")_(xrarrpi/2)f(x)=oo (c) ("lim")_(xrarrpi/2)f(x)=o (d) none of these

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

If ("lim")_(xtoa)[f(x)g(x)] exists, then both ("lim")_(xtoa)f(x)a n d("lim")_(xtoa)g(x) exist.

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

("lim")_(xvec0)1/xcos^(-1)((1-x^2)/(1+x^2)) is equal to (a)1 (b) 0 (c) 2 (d) none of these