Thread: Cauchy definition (epsilon-delta) of continuous functions

Hi can someone please help with this question:



What i Know

I know that this graph is not continuous at a=0 but i am finding it difficult to prove this using Cauchy definition (epsilon-delta) of continuous functions.

Thanks Subzero

Originally Posted by SubZero

Hi can someone please help with this question:



What i Know

I know that this graph is not continuous at a=0 but i am finding it difficult to prove this using Cauchy definition (epsilon-delta) of continuous functions.

Thanks Subzero

Good! You are probably finding it difficult to show that function is not continous at 0 because it is continuous at 0!

Given any if x> 0, f(x)= x so we can just take . That way, "if , ". While if x< 0, f(x)= 0 so for any x and so for .

(The function is not differentiable at x= 0 but is continuous there.)

Thanks for the help