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`

If [dot] denotes the greatest integer function, then (lim)_(xvec0)x/a[b/x] a. b/a b. 0 c. a/b d. does not exist

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)(cosx) is discontinuous at x=0 (b) continuous at x=0 (c) differentiable at x=0 (d) none of these

If f(x)=([x])/(|x|),x ne 0 where [.] denotes the greatest integer function, then f'(1) is

The function f(x)=sin^(-1)(cosx) is (a) . discontinuous at x=0 (b). continuous at x=0 (c) . differentiable at x=0 (d) . non of these

If f(x)={(x-|x|)/x ,x!=0, 2,x=0 , show that lim_(xrarr0) f(x) does not exist.

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

Let f(x) be a twice-differentiable function and f"(0)=2. The evaluate: ("lim")_(xvec0)(2f(x)-3f(2x)+f(4x))/(x^2)

Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2 .

If f(x)=([x])/(|x|), x ne 0 , where [.] denotes the greatest integer function, then f'(1) is