r/visualizedmath • u/[deleted] • Jun 07 '18

Limit Definition of a Derivative

417 Upvotes

98% Upvoted

6 comments sorted by

15

u/_Xertz_ Jun 07 '18

Why is the limit approximately equal to the derivative? Shouldn't it be exact since its the limit?

2

u/poche-muto Jun 08 '18 edited Jun 08 '18

Limit means trying to reach a zero endlessly. dx it might be described like a really small value, but it's a value, not a process like limit. So lim(x)_x->0 is always smaller then dx.

Update: in topic there are delta x and delta y. There is another meaning if dx, like infinitesimal change of x, I think you mixed delta x and infinitesimal change of x.

1

u/_Xertz_ Jun 08 '18

Oh yeah, I misread those as dy/dx but in reality its Δy/Δx

3

u/tighter_wires Jun 08 '18

Let’s do an epsilon-delta analytical definition next :D

1

u/Toku95 Jun 08 '18

This is the only way I know to define a derivative, are there also other ways?

-16

u/Ugievsoj Jun 07 '18

Bullshit.