Simple limits problem

1. Sep 15, 2006

__redzone

I'm given the limit f(x + $$\Delta$$x) / $$\Delta$$x
Given f(x) is 2x + 3, do I just plug in 2x +3 into x? Or do I plug it into x and $$\Delta$$x, or do I find the limits of f(x + $$\Delta$$x) / $$\Delta$$x) and -f(x)/$$\Delta$$x?, etc..If someone could get me started on this it would be great, Thanks.

2. Sep 15, 2006

arildno

First of all, write your problem CORRECTLY from your book. That you haven't done.

3. Sep 15, 2006

__redzone

This is my first time using latex so I guess I'll just type it out for clarity. Find the limit of the function (f(x + delta x) - f(x)) / delta x as delta x approaches 0 when f(x) = 2x + 3.

4. Sep 15, 2006

arildno

Quite so.
Given that, what is in this case f(x+delta x)?

5. Sep 16, 2006

HallsofIvy

You are going to find it very, very difficult to do calculus if you don't understand what "f(x)" and "f(x+ y)" mean!

If f(x)= 2x+ 3, then f(a)= 2a+ 3 (just replace x in the entire formula with whatever is in the parentheses on the left). In particular, f(x+ y)= 2(x+ y)+ 3= 2x+2y+ 3.

(Your latex was fine in your first post. arildno's point was that you didn't specify "as $\Delta$x goes to 0"!)

6. Sep 16, 2006

arildno

Actually, he did not subtract f(x) in the numerator; that's what I reacted upon.