$\Delta x$ in limit problem?

real-analysis calculus limits

I was working on some limit homework and everything was going fine until I reached this problem:

$$\lim_{\Delta x \to 0} \frac{2(x + \Delta x) - 2x}{\Delta x}.$$

I am understanding limits but the triangle (delta?) before the x is throwing me off. I have never seen it used this way before and I have no idea what it means in this context. Could anyone help me out? Thanks.


For the sake of having an answer: $\Delta x$ is just the name of a variable whose meaning is supposed to be "a small change in $x$." It is not, as I guess one might think, some kind of strange function of $x$ or anything like that.


The Derivative of a function $f(x)$ denoted by $f'(x)$ is defined as the limit $$f'(x) = \lim_{\Delta{x} \to 0} \frac{f(x + \Delta{x}) - f(x)}{\Delta{x}}$$

So you limit is the derivative of the function $f(x)=2x$. Geometrically, derivative of a function can be seen in this picture: enter image description here

Good picture which was given at Wikipedia link: enter image description here

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