Let `f(x)={x+1,\ if\ x >0, x-1,\ if\ x<0dot` Prove that `("lim")_(x->1)\ f(x)` does not exist.

Let f(x)={x+1,\ if\ x >0, and x-1,\ if\ x 1)\ f(x) does not exist.

Let f(x)=\ {x+5,\ if\ x >0 and x-4,\ if\ x 0)\ f(x) does not exist.

Let f(x)={x+1,quad if quad x>0,x-1,quad if x<0 Prove that (lim)_(x rarr1)f(x) does not exist.

If f(x)=(|x-1|)/(x-1) prove that lim_(x rarr1)f(x) does not exist.

Let f(x) be a function defined by f(x) = {{:((3x)/(|x|+2x),x ne 0),(0,x = 0):} Show that lim_(x rarr 0) f(x) does not exist.

let ( f(x) = 1-|x| , |x| 1 ) g(x)=f(x+1)+f(x-1)

Suppose that f(x) is a differentiable function such that f'(x) is continuous, f'(0) = 1 and f"(0) does not exist. Let g(x) = xf'(x). Then

Statement - I: if lim_(x to 0)((sinx)/(x)+f(x)) does not exist, then lim_(x to 0)f(x) does not exist. Statement - II: lim_( x to 0)(sinx)/(x)=1

Suppose that f(x) is a differentiable function such that f'(x) is continuous, f'(0)=1 and f''(0) does not exist. Let g(x) = xf'(x). Then