### Home > PC3 > Chapter 9 > Lesson 9.1.4 > Problem9-85

9-85.

This problem is a checkpoint for evaluating limits from graphs and tables.

1. Use the piecewise-defined function, $f$, graphed at right to evaluate each of the limits below.

1. $\lim\limits_{x \to -5}f(x)$

1. $\lim\limits_{x \to -2^-} f ( x )$

1. $\lim\limits_{x \to 1} f ( x )$

1. $\lim\limits_{x \to 1^+} f ( x )$

1. Use the piecewise-defined function, $f,$ graphed at right to evaluate each of the limits below.

2. Let $f(x)=\frac { 4 ^ { x } - 3 ^ { x } } { x }$. Copy and complete the table of values below to estimate the value of $\lim\limits_{x \to 0} \frac { 4 ^ { x } - 3 ^ { x } } { x }$.

 $x$ $–0.01$ $–0.001$ $–0.0001$ $0.0001$ $0.001$ $0.01$ $f(x)$

Ideally at this point you are comfortable working with these types of problems and can complete them correctly. If you feel that you need more confidence when completing these types of problems, then review the Limits Checkpoint materials available at cpm.org and try the practice problems provided. From this point on, you will be expected to do problems like these correctly and with confidence.

Answers and extra practice for the Checkpoint problems are located in the Reference Tab of your eBook.