Limits - true and false help

I can do limits - but not when it comes to true and false:

1. if lim X->0 f(x) = 0, then there exists c such that f (c) <.001

2. f is undefined for x=c, then lim x-> c f (x) does not exist

3. If lim x->c f (x) = L and f(c) = L then f is continuous at c

4. If f(x) = g(x) for x not equal to c and f(c) not equal to g(c) then f or g must be discontinuous at c

5. If f is continuous on (a,b], then f must take on both a maximum and minimum on (a,b]

6. Rational functions have infinitely many discontinuities.

7. Trigonometric functions can have infinitely many discontinuities.

If you can help explain any or all of those to me, I would be thankful.