Estimating limits using tables involves analyzing the behavior of a function $f(x)$ as $x$ approaches a specific value $c$. We create a table of $x$ values that get progressively closer to $c$ from both the left and the right, and then observe the corresponding $f(x)$ values. If the $f(x)$ values approach a specific number $L$ from both sides, we estimate that the limit of $f(x)$ as $x$ approaches $c$ is $L$. This method is particularly useful when the function is difficult to evaluate directly at $x = c$, or when the function is defined piecewise.
This technique provides a numerical approximation of the limit. It’s important to choose $x$ values that get sufficiently close to $c$ to get an accurate estimate. The closer the $x$ values are to $c$, the better the approximation of the limit will be. Be aware that this method provides an estimation, not an exact value, and it may not always be accurate, especially if the function oscillates rapidly near $c$.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Limit | A. The value that a function approaches as the input approaches some value. |
| 2. Function | B. A relation where each input has exactly one output. |
| 3. Estimate | C. To find an approximate value. |
| 4. Table | D. An arrangement of data in rows and columns. |
| 5. Approach | E. To get closer to a value. |
When estimating limits with tables, we examine values of $x$ that get progressively ______ to a specific value, $c$, from both the left and the ______. If the corresponding $f(x)$ values ______ a specific number, $L$, from both sides, we ______ that the limit of $f(x)$ as $x$ approaches $c$ is $L$. This method is useful when direct ______ is difficult.
Explain a situation where using a table to estimate a limit would be more beneficial than trying to calculate it algebraically.
Please log in to post your answer.
Log InEarn 2 Points for answering. If your answer is selected as the best, you'll get +20 Points! 🚀