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Online Tutorial -
CG50: How to Use Table Mode

Video Transcript

In this tutorial, we'll be looking at table mode, how to use it and what it might be useful for. It creates a table of values for a function, which actually turns out to be surprisingly useful. It's essentially the same as table mode on the Casio scientific calculators, but has the option to display the gradient, as well as the y coordinates, in the table of values for up to two functions. To work along with this tutorial, you may find it easiest to reset the calculator before starting, so that your screen matches the one in the video. If you decide not to, you will find the functions you have typed in graph mode will already appear in table mode as well.

So go to table mode and type in the function you want using the X Theta T key for x. Press enter and then go to set to specify the lowest and highest values for x and the step size. Press enter to create the table and scroll down to see the rest of the values.

Sometimes it's useful to see the value of the gradient at each point as well, so the gradient function can be switched on.

Go to setup and then scroll down until you get as far as derivative. And then choose on and execute. And now create the table of values and you'll see the derivative at each point is given in the third column. Differentiation gives the gradient of 2x minus 7 and a useful way of checking that this is in fact correct is to enter another function alongside the one we already have.

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Exit the table and type 2x minus seven as your second function. When you execute, it creates a table where you can compare the answers. The table has two identical columns. Pretty strong evidence that the derivative of 2x minus seven is right. Table mode makes decimal search a very easy method for solving equations. By zooming in on the interval containing the root, evidence can be found for the root to as many decimal places as necessary. Exit and delete the existing functions.

And now type in the function which is equal to zero in the equation to be solved. Choose settings for the start and the end and the step size. And execute. When you view the table, you can see there's a change in sin of y as x goes from 2.1 to 2.2, which is evidence that there is a root of the equation between these values. To find the root more accurately, zoom in by changing the settings so that the start is 2.1 and the end is 2.2.

And then reduce the step size to 0.01. Enter to create the table and scroll down again to see the change in sin of y. We can now see that the root lies between 2.15 and 2.16. This process can be repeated as many times as necessary to get the required degree of accuracy. It's always a good idea to find the root to one more decimal place than the question asks and then round it.

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