Use a graphing utility to graph the function. Then use the trace or table feature to identify the limit.
lim 5/x-2 x-->2
I know I posted this question before but I am still having a hard time doing this. I pressed the y= button and typed the normal equation in: 5/x-2. Is this correct and if so now what do I do?
Yes, you have correctly entered the equation 5/(x-2) into the graphing utility. After entering the equation, you will now graph it to visualize the function.
To graph the function using the graphing utility, follow these steps:
1. Press the "Graph" or "Draw" button on the calculator to display the graph of the function on the coordinate plane.
Now, to use the trace or table feature to identify the limit, you can follow either of the two methods:
Method 1: Using the Trace Feature
1. Press the "Trace" or "T" button on the calculator.
2. Move the cursor along the graph using the arrow buttons or the arrow keys.
3. As you approach the x-value of 2, observe the corresponding y-values on the screen.
4. The limit is the value that the y-values approach as x gets closer and closer to 2. You may notice that the y-values approach positive infinity (∞) as x approaches 2 from the right (x > 2) and approach negative infinity (-∞) as x approaches 2 from the left (x < 2).
5. Thus, the limit as x approaches 2 is undefined or does not exist.
Method 2: Using the Table Feature
1. Press the "Table" or "Tbl" button on the calculator.
2. Enter x-values that are very close to 2. For example, you can start with x = 2.1, 2.01, 2.001, 2.0001, etc.
3. Observe the corresponding y-values in the table.
4. As the x-values get closer and closer to 2, you'll notice that the y-values become larger and larger (positive infinity) for x-values greater than 2. Similarly, the y-values become smaller and smaller (negative infinity) for x-values smaller than 2.
5. Hence, the limit as x approaches 2 is undefined or does not exist.
Remember that the graphing utility provides a visual representation of the function and helps you understand the behavior of the function near certain values. In this case, we see that the function becomes unbounded (approaches infinity or negative infinity) as x approaches 2.