# Limits question(s)

1. Sep 20, 2011

### Nitrate

1. The problem statement, all variables and given/known data
Find the following limits, if they exist:

h) lim absolute value[x]/(x)
x->0$^{+}$

and

i) lim absolute value[x]/(x)
x->0$^{-}$

2. Relevant equations
Not sure

3. The attempt at a solution
The answer to h) [according to the back of the textbook] is 1
and the answer to i) is -1.
I'm really not sure how to arrive at those answers.

2. Sep 20, 2011

### dynamicsolo

What does the absolute value operation do to positive numbers? to negative numbers?

3. Sep 20, 2011

### flyingpig

WHat is the definition of the absolute value!?

4. Sep 20, 2011

### Nitrate

Positives stay the same and negatives turn to positives, but I'm not sure how this will help me.

5. Sep 20, 2011

### dynamicsolo

So if x is any positive number, what will | x | equal? What will $\frac{|x|}{x}$ equal?

If x is any negative number, what will | x | equal? And now what will $\frac{|x|}{x}$ equal?

6. Sep 20, 2011

### Nitrate

The distance of x from 0.

7. Sep 20, 2011

### Nitrate

I see it now, but why can x be ANY positive number for the first question and ANY negative number for the second? I thought you had to substitute the zero into the x variable.

8. Sep 20, 2011

### dynamicsolo

Because we are not just plugging numbers into the function; we are looking to see what happens as x takes on (any) positive or negative values that are getting closer and closer to zero. (This is important because it is often the case in limit problems (like this one) where putting the "limiting value of x" into the function won't tell you anything useful at all...)

9. Sep 20, 2011

### Nitrate

How can I tell what the graph of abs(x)/(x) looks like? [I've already used my graphing calculator, but I want to find out how to do it without my calculator] I know that the abs(x) by itself looks like a v opening up.

10. Sep 20, 2011

### dynamicsolo

All right, what sort of graph do you get if you take the values of y = abs(x) and divide them by the value of x at each point?