Let `f(x)=\ {x+5,\ if\ x >0x-4,\ if\ x<0` Prove that `("lim")_(x->0)\ 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,\ if\ x >0, and x-1,\ if\ x 1)\ f(x) does not exist.

Let f(x)={x+5,quad if x>0x-4, if x<0 Prove that (lim)_(x rarr0)f(x) does not exist.

If f(x) = (|x|)/x then show that Lt_(x to 0) f(x) does not exist.

If f(x)=sgn(x)" and "g(x)=x^(3) ,then prove that lim_(xto0) f(x).g(x) exists though lim_(xto0) f(x) does not exist.

If f(x)=sgn(x)" and "g(x)=x^(3) ,then prove that lim_(xto0) f(x).g(x) exists though lim_(xto0) f(x) does not exist.

If f(x)=sgn(x)" and "g(x)=x^(3) ,then prove that lim_(xto0) f(x).g(x) exists though lim_(xto0) 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.

Show that f (x) = |x| is continuous at x= 0 but f'(0) does not exist

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