Perspective Realisation:
So far, we’ve been interpreting limits without even realising it. The term actually has the idea of a limit built in. As you make a tiny change thats so tiny (so tiny it may even be approaching 0 😉), you can get the derivative / slope of a function.
Formal Definition
This is nice because it avoids the paradox of “infinitely small”.
There’s also an Epsilon Delta definition 😞.
ED Definition
Imagine an input range and output range. If you shrink the input range enough, then the corresponding output range should also still be able to shrink. Thus there’s a defined limit.
There’s also the idea of L’Hopital’s Rule.
Limit Laws:
