If [.] is the greatest integer function and `f(x)=[tan^2x],` then `(a) ("lim")_(xvec0)f(x)` does not exist `(b) f(x)` is continuous at `x=0` `(c) f(x)` is not differentiable at `x=0` `(d) f^(prime)(0)=1`

Let f(x)={[x]x in I x-1x in I (where [.] denotes the greatest integer function) and g(x)={sinx+cosx ,x<0 1,xgeq0 . Then for f(g(x))a tx=0 (lim)_(xvec0)f(g(x)) exists but not continuous Continuous but not differentiable at x=0 Differentiable at x=0 (lim)_(xvec0)f(g(x)) does not exist f(x) is continuous but not differentiable

The function f(x)=sin^(-1)(cos x) is discontinuous at x=0 (b) continuous at x=0( c) differentiable at x=0 (d) none of these

Let f(x) = [tan?x], (where [] denotes greatest integer function). Then -(B) f(x) is continuous at x = 0.(A) lim f(x) does not exist(C) f(x) is not differentiable at x = 0(D) f'(0) = 1nail futhara (denotes the greatest intege

f(x) = [x] (greatest integer function ) is continuous at x = 0 then f(0) = ?

If f(x)=xs in(1/x),x!=0 then (lim_(x rarr0)f(x)= a.1b*-1 c.0 d.does not exist

Prove that the greatest integer function defined by f(x)=[x],0

Let f(x)=[x], where [.] is the greatest integer fraction and g(x)=sin x be two valued functions over R. Which of the following statements is correct? (a) Both f(x) and g(x) are continuous at x=0 (b) f(x) is continuous at x=0, but g(x) is not continuous at x=0. (c) g(x) is continuous at x=0, but f(x) is not continuous at x=0. (d) Both f(x) and g(x) are discontinuous at x=0

If f(x) is continuous at x=0 , where f(x)=(1-cos 3x)/( x tan x) for x != 0 , then f(0)=

Consider the following in respect of the function f(x)={{:(2+x","xge0),(2-x","xlt0):} 1. lim_(x to 1) f(x) does not exist. 2. f(x) is differentiable at x=0 3. f(x) is continuous at x=0 Which of the above statements is /aer correct?

Let [.] denotes G.LP. for the function f(x)=(tan (pi[x-pi])/(1+[x]^2)) the wrong statement is (A) f(x) is discontinuous at x=0 (B) f(x) is continuous for all values of x (C) f(x) is continuous at x=0 (D) f(x) is a constant function