Find the limit of $f(x)$ as $x$ approaches $3$ from the left
By Michael Henderson •
$$f(x)=\begin{cases} {0} & \text{if $x<3$} \\x+1 & \text {if $3\le{x}\le4$}\\ 5 & \text{if $x>\ 4$} \\ \end{cases}$$
As it asks me to approach $3$ from the left I concluded that the answer would be $0$ as if it is $x<3$, $f(x)=0$. This seems too easy however so I would like to know if I did something wrong and what I can correct if I did do this question incorrectly.
$\endgroup$ 11 Answer
$\begingroup$You are correct. $$lim_{x->3^{{-}}}f(x)=0$$
Remember that $x%$ approaches $3$ but never reaches it.
Thus $x$ is always in the domain of the part if $x < 3$
Note that you are only correct because from the left
Since the limit from the right is equal to $4$. The limit actually doesn't exist. But the 1 sided limits do.
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