Limits

[loud valve]

I don't understand limits at all

[velvet pebble]

The basic idea of a limit is what happens as you get closer to a certain number. so called "approach".

[loud valve]

So basically we are trying to understand the behaviour of a function at a certain point

Is it

correct

[velvet pebble]

More like close to that point

[loud valve]

I see

[velvet pebble]

Its useful when the function is undefined on that point and in many other cases

[drowsy apex]

You are trying to understand the local behavior of a function near a point, but not necessarily at that point

[echo helm]

One example is $y = \frac{x(x + 4)}{x + 4}$

[past atlas]

King Leo

[echo helm]

$$\lim_{x \to 4}y = 4$$
Because $y$ simplifies to just $y = x$.

[past atlas]

King Leo

[echo helm]

*-4

[drowsy apex]

In the simplest example, consider $f(x)=1$ if $x=0$, and $f(x)=0$ otherwise. Around $x=0$ (but not exactly it), all $f(x)$ are located near $y=0$. This is the limiting behavior

[past atlas]

SWR

[loud valve]

Understood it completely, ty