This may just be a forgetful moment on my part, but could someone please explain to me how you get...

Question

anonymous · Answer

$$f(x)=3x^2+2$$ from $$3x^2+3x \Delta x+ \Delta x^2+2$$
by substituting the limit (0) into the equation?

anonymous · Answer

I'm learning derivatives if that helps explain anything.

zehanz · Answer

The limit means $\Delta x $ becomes smalles and smaller.
Now, 3x has a certain value, once you have chosen the x.
Imagine what happens with the term $3x \cdot \Delta x$: you have to multiply this certain value of 3x with an ever smaller number: it becoms vanishingly small, in fact it goes to 0.
Same happens to $ (\Delta x)^2$, leaving you with $3x^2 + 2$.

anonymous · Answer

So only the $$x \Delta$$ will be substituted with the 0, correct?

amistre64 · Answer

yes

anonymous · Answer

Is there a particular reason why? (sorry, but if i know why it helps me remember to do it)

anonymous · Answer

Oops! Never mind! I see now.
Thank you.

zehanz · Answer

yw!