calculate the limit of the following functions and prove directly from definition (using $\epsilon$ and $\delta$)
a) $\lim _{x\to 2}(x^3+3x)$
We just learned the definition of limits in regards to function and this is supposed to be a simple question. But I just can't understand how to use the info I'm given.
a) Am I right with guessing the limit is $2^3+3\cdot 2=14$?
b) Assuming I am (I don't think it would change much if I am not), then for an $\epsilon$ I want to find a $\delta$ such that for each $x$ in the punctured environment of $(x_0 - \delta,x_0+\delta)$ , $|x^3+3x-14|<\epsilon$, but I have no idea how to proceed from here. I tried searching for similar examples to see how the truth process is done but wasn't able to find any.