# Limits - true and false help

• Sep 28th 2009, 11:21 AM
BooGTS
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.
• Sep 28th 2009, 01:53 PM
stapel
Use the definitions and intuitive meanings of the terms and processes:

Quote:

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

...|f(c) - 0| < (some small value).

Quote:

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"?

Quote:

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"?

Quote:

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)?

Quote:

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?

Quote:

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?

Quote:

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?

(Wink)