# Thread: Limits - true and false help

1. ## 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.

2. Use the definitions and intuitive meanings of the terms and processes:

Originally Posted by BooGTS
1. if lim X->0 f(x) = 0, then there exists c such that...
...|f(c) - 0| < (some small value).

Originally Posted by BooGTS
2. f is undefined for x=c, then lim x-> c f (x) does not exist
Is "limit exists at" the same thing as "continuous at"?

Originally Posted by BooGTS
3. If lim x->c f (x) = L and f(c) = L then f is continuous at c
What is the definition of "continuous"?

Originally Posted by BooGTS
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
Suppose that f is continuous at c, so that lim, x->c, f(x) = f(c). What does this tell you about g(c)?

Originally Posted by BooGTS
5. If f is continuous on (a,b], then f must take on both a maximum and minimum on (a,b]
Take a close look at the definitions and theorems. Does this half-open interval fulfill the requirements for this conclusion?

Originally Posted by BooGTS
6. Rational functions have infinitely many discontinuities.
Think about a rational function you've graphed recently, like in your algebra class. Did you draw infinitely-many vertical asymptotes?

Originally Posted by BooGTS
7. Trigonometric functions can have infinitely many discontinuities.
Think about the trig functions you've graphed. What do a couple of them look like, with respect to vertical asymptotes?