# Precise Definition of a limit

1. Sep 14, 2009

### step1536

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

How close to 2 do we have to take x so that 5x+3 is within a distance of 0.075 from 13.
I am confuse on how to evaluate this problem.

2. Sep 14, 2009

### VeeEight

You should state your question more clearly.

A distance of 0.075 from 13 can be 13 + 0.075 or 13 - 0.075. Can you find an x such that 5x+3 evaluates to one of those two points?

3. Sep 14, 2009

### HallsofIvy

Staff Emeritus
5x+3 will be within distance 0.075 from 13 (above or below) as long as 5x+ 3 is between 13- 0.75 and 13+ 0.75 or $12.25\le 5x+ 3\le 13.75$. Solve that inequality for x. How close is that to 2?

4. Sep 14, 2009

### step1536

I understand that part but how do you work the problem out?

5. Sep 14, 2009

### step1536

so x=1.85,2.15; then I would then subtract 2-1.85 and 2-2.15. my answer would be .15

6. Sep 14, 2009