Limits

[Nato]

i know that limits are covered a little in units 1/2, but are they going to be necessary in units 3/4.
is it worth learning them?

[pi]

You'll use it if they ask you to diff something via first principles. I found it also helps with some graphing techniques too.

[Planck's constant]

Not in the Study Design, AFAIK.
Limits are only used in conjunction with the formal definition of the derivative, continuity and differentiability.

[abeybaby]

I like to teach basics of limits to help with when then gradient is defined, and continuity, but thats it

[FlorianK]

Actually not, but limits are cool for proving stuff like derivatives or integrals

[QuantumJG]

i know that limits are covered a little in units 1/2, but are they going to be necessary in units 3/4.
is it worth learning them?

Is there anything about limits you would like to know?

For example:

The limit of a function , at a point is defined as:



A function is continuous at a point , if there exists a finite valued number , such that



So in your mind you should think of a continuous function as something that has no "jumps" in it.

Those are all continuous functions



This is a discontinuous function



The derivative of a function is defined as:



A function is differentiable at a point , if:



This is a differentiable function



This isn't a differentiable function



Note: Differentiability implies continuity, but continuity doesn't imply differentiability.

[Stick]

I just remember continuity and differentiability using anecdotes:

"If a function is continuous, I shouldn't have to lift the pen off the page."

"If a function is differentiable, it must be continuous, but also have no cusps."

"Can I draw multiple tangents on a point? If so, it's a cusp and the function is not differentiable."

[Azerel]

Limits are quite useful just to understand the concept of differentiation