lim (Δx^2 - 2Δx) / Δx x->0

You are confusing me with the deltas    Is this what you want?

$$\lim\limits_{\Delta x\rightarrow0} \frac{\Delta x^2-2\Delta x}{\Delta x}\\\\
=\lim\limits_{\Delta x\rightarrow0} \frac{\Delta x(\Delta x-2)}{\Delta x}\\\\
=\lim\limits_{\Delta x\rightarrow0} \frac{(\Delta x-2)}{1}\\\\
=\lim\limits_{\Delta x\rightarrow0} \Delta x-2\\\\
=0-2\\\\
=-2$$

Help please!

YES! Thank you! ^_^

That is good :)