Question

Why is the derivitive the limit of f(x) as the change in x approaches 0?

Answer 1

here is the pdf. i hope it helps

Answer 2

The derivative is the slope of the line tangent to a curve at a given point. Graphically, picture a curve (i.e. your basic exponential function) with a secant line running through it. So as the distance between the two intersections gets smaller and smaller so that they're right next to each other and the gap becomes almost 0 (aka change in x goes to 0), the two intersections "overlap" so that your secant line becomes a tangent line. Therefore the derivative of f(x) occurs when/as x approaches 0. Cheers!

Answer 3

I'm just on session 2 here, but I also remember "Slide Rule Calculus" (am I showing my age?) ...

We have to sneak up on the answer, using the limit as the "change in x" or "delta x" approaches zero, because we can't calculate it when that "change in x" is equal to zero, because we'd end up dividing by zero.

Once we set up our equations, and cancel out (remove "delta x" (change in x) from the denominator, we can figure out our answer, because we can then use zero for all other "delta x" values.

Hope this helped a little.

John (re-watching clips to make sure I can do the work and the samples that they present)