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

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

If f(x)=|x-1|-[x], \where\ [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")_(x to1)f(x) exists (D) ("lim")_(x to1)f(x) does not exist

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-

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)=0 (d) none of these

If f(x)=2|x|-3[x] where [x] denotes greatest integer in x not exceeding the value of x, find the value of f(2.5) and f(-2.5).

If f(x)= x-[x],x(phi0)inR , where [x] is greatest integer less than or equal to x, then the number of solution of f(x)+f(1/x)=1 are

If lim_(x->a)[f(x)g(x)] exists, then both lim_(xtoa)f(x) and lim_(x->a)g(x) exist.

If f(x)={{:((x-|x|)/(x)","xne0),(2", "x=0):}, show that lim_(xto0) f(x) does not exist.

If f(x)=(3x^2+a x+a+1)/(x^2+x-2), then which of the following can be correct (a) ("lim")_(x-> 1)f(x) for a=-2 (b) ("lim")(x->-2)f(x) for a=13 (c) ("lim")(x-> 1)f(x)=4/3 (d) ("lim")(x->-2)f(x)=-1/3

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