Limits

$$\underset{x\to c}{\lim }f(x)=L$$ $$(\forall ϵ>0)(\exists \delta >0)(\forall x\in \Re )(0<|x-c|<\delta ⟹|f(x)-L|<ϵ)$$

$f(x)$ is near $L$ , when $x$ is suitably near c.

Understand the definition, and move on.
LIMIT THEOREMS

https://personal.math.ubc.ca/~marcus/Math120/Math120_Lectures7-10.pdf
Proofs seem to be mostly algebra tricks :(

Proofs

1. Goal is to pick a $\delta$ in terms of $ϵ$ , and write $f(x)-L$ in terms of $x-c$
2. Then you can do algebra to show $f(x)-L$ is less than some modification of $\delta$
3. Then substitute $ϵ$ for $\delta$
4. To show the function error from limit is less than $ϵ$

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