Hi, can some one please provide me an example for each basic limit here in the photo. I can't grasp the idea with variables. Thank you!
Edit: I have an extra question, If we find a limit and we get any number except 0, So 5/0 is our limit undefined? Or must we manipulate it that we do not have a 0 on the denominator. I know that if we get 0/0 that is indeterminate form and we must manipulate the limit.
If you don't get the general rule, substitute a number and contemplate the specific. All these rules just let you compute complex limits from simpler ones.
$\displaystyle \lim_{x \rightarrow 2}\{(x + 3)^2\} = \{\lim_{x \rightarrow 2}(x + 3)\}^2 = 5^2 = 25.$
$\displaystyle \lim_{x \rightarrow a}f(x) = b \ne 0\ and\ \lim_{x \rightarrow a}g(x) = 0 \implies \lim_{x \rightarrow a}\dfrac{f(x)}{g(x)}\ is\ undefined.$