Chapter 2.4, Problem 1E

Finding Limits Graphically

Which of the following statements about the function $y=f\left(x\right)$ graphed here are true, and which are false?

1. $\underset{x\to -1^{+}}{\lim }f\left(x\right)=1$

2. $\underset{x\to 0^{-}}{\lim }f\left(x\right)=0$

3. $\underset{x\to 0^{-}}{\lim }f\left(x\right)=1$

4. $\underset{x\to 0^{-}}{\lim }f\left(x\right)=\underset{x\to 0^{+}}{\lim }f\left(x\right)$

5. $\underset{x\to 0}{\lim }f\left(x\right)\text{exists}.$

6. $\underset{x\to 0}{\lim }f\left(x\right)=0$

7. $\underset{x\to 0}{\lim }f\left(x\right)=1$

8. $\underset{x\to 1}{\lim }f\left(x\right)=1$

9. $\underset{x\to 1}{\lim }f\left(x\right)=0$

10. $\underset{x\to 2^{-}}{\lim }f\left(x\right)=2$

11. $\underset{x\to -1^{-}}{\lim }f\left(x\right)$ does not exist.

12. $\underset{x\to 2^{+}}{\lim }f\left(x\right)=0$