One Sided Limits Practice Problems

Problem: One Sided Limits #1

The plot of $f(x)$ is shown below. (Not to scale)

For each of the points given below, find $\lim_{x\to a^-}f(x)$ , $\lim_{x\to a^+}f(x)$ , $\lim_{x\to a}f(x)$ , and $f(a)$ .

1) $a = 1$
2) $a = 2$
3) $a = 3$
4) $a = 4$

Problem: One Sided Limits #2

Sketch a function which satisfies all of the following criteria:

1. $\large{\lim_{x\to 4^-}f(x) = 2}$

2. $\large{\lim_{x\to 4^+}f(x) = 4}$

3. $\large{f(4)=}$ Does not exist

4. $\large{\lim_{x\to 1}f(x) = 5}$

5. $\large{f(1) = 1}$

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