When do you use limit notation?
My teacher is a stickler for correct notation. When evaluating a limit, when do you stop using the limit notation $\lim \limits_{x\to c}\left(f(x)\right)$ and just write a value?
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$\begingroup$You stop using it if and when you actually evaluate the limit, i.e. in circumstances where a limit exists and is finite, and you are recording its initial evaluation $L$. $$\lim_{x\to c} f(x) = L$$
If the limit does not exist, you can write something to the effect $$ \lim_{x\to c} f(x) \;\text{does not exist.}$$
If the limit diverges to (+) infinity, e.g., you might write something to the effect $$\lim_{x\to c} f(x) \; \text{diverges to } \infty$$ though in the divergent case, when the limit diverges to (+) infinity, e.g., you'll sometimes see $\lim_{x\to c} f(x) \to \infty,\;$ or $\;$"as $x\to c$, $f(x) \to \infty$." Follow your instructor's lead here, in this scenario.
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