# Homework Help: Limit help

1. Feb 1, 2006

### ussjt

diagram: http://img.photobucket.com/albums/v629/ussjt/math3.jpg

A thin equilateral triangular block of the side length 1 unit has its face in the vertical xy-plane with vertex V at the origin. Under the influence of gravity, it will rotate about V until a side hits the x-axis floor (see diagram). Let x denote the inital x-coordinate of the midpoint M of the side opposite V, and let f(x) denote the final x-coordinate of the point. Assume that the block balances when M is directly above V.

(a) Determine the domian and range of f
(b) Where on the domain is f discontinuous
(c) Identify any fixed points of f

I have no clue how to go about answering the question. Any help/hints on solving each part would be great, thanks.

2. Feb 1, 2006

3. Feb 1, 2006

### VietDao29

You labelled the thread limit help, but I see no limit in your problem... Am I missing something?
First off, do you understand what the problem says? It says you will have different M's initial positions if you place the triangle differently, in other word, you will have different x if you place the triangle differently. And for every position, you will have a final position for M (namely f(x)). So for every x, you have one f(x). Is f(x) a function of x?
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Before tackling the problem, let's answer some questions:
1. So what is x if M is right above V? What's f(x) in that case?
2. If x > 0, then what happen to the triangle? What's f(x) in that case?
3. If x < 0, then what happen to the triangle? What's f(x) in that case?
4. So what's the range of f?
5. What's the maximum value x can have? What's the minimum value?
6. So what's the domain of f?
7. From question 1 to 3, where on the domain is f discontinuous?
8. What's the definition of a fixed point? From here, can you point out the fixed points?

4. Feb 1, 2006

### ussjt

Sorry about the name, that is what the title was on the page in the book.

I am a little confused still, so for the range, do you mean the highest point m will reach to the lowest(which is 0,1). Also for the domain, I am really confused about that part.

5. Feb 2, 2006

### VietDao29

Okay, I think you should read the problem again, and then my post. Then can you please try to answer all of them one by one (from 1 to 8), so that I can know what you don't understand.
If M is place slightly to the negative x-axis (i.e x < 0), will the triangle rotate clockwise, or counter-clockwise? When it reaches the x-axis, it stops rotating, what's the x-coordinate of M at that time? What's f(x)?
If M is right above V (it means its initial x-coordinate is 0, x = 0), will it rotate? So what's f(0)?
If M is slightly to the positive x-axis (i.e, x > 0). What's f(x), the final x-coordinate of M?
Do you fully understand what the question asks now?

Last edited: Feb 2, 2006