Look at a graph of y=1/x near x=0, you will see that it goes to +infty as you

approch 0 from above and -infty as you approach 0 from below, so near 0

a small change in x cn result in a large change in y, hence this is

discontinuous at x=0.

For you other example if you change x to x+e, y changes from x*2 to

x*2+e*2, and as e is small so is e*2.

Note by convention in ASCII (plain text) * denotes multiplication. If you

meant x squared you should use x^2. In this case y changes from x^2 to

(x+e)^2 = x^2 + 2e x + e^2, and if e is small enough 2e x+e^2 is also

small.

RonL