Question

How do limits work in calculus?

Answer 1

The same way they work in Pre-Calculus.

Limits convey the action of approaching a coordinate in a graph that may or may not exist in the curve itself, whether it's due to an asymptote or a discontinuity. It tends to describe a value that you are unsure exists and can be used as a systematic way of determining whether or not it does. You can approach from the left or right in a `y = f(x)` graph.

For example:
`lim_(x->0^+) 1/x = oo`
"The limit as x approaches 0 from the positive/right side of `1/x` is infinity"

`lim_(x->0^-) 1/x = -oo`
"The limit as x approaches 0 from the negative/left side of `1/x` is negative infinity"

`lim_(h->0) [f(x+h) - f(x)]/h`
"The limit as `h` approaches a very small number from either side of `(f(x+h) - f(x))/h` is the slope of the function `h` units away from the point of examination"

which basically says that if you zoom in very far into a function, it looks linear and you can use the basic slope formula at that close zoom to find the slope. `h` is some very small value, hence the `h->0`.