Solving Simple Limits with Examples

[__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.

 

[arildno]

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

 

[__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.

 

[arildno]

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

 

[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"!)

 

[arildno]

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