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User Guide: Contents Page Index of Functions

| # Calculus & Intersection Points
You can calculate numerical integrals, derivatives (dy/dx) and x-axis intercepts with any X-Y style chart. In addition, you can find intersection points of dual function plots. Use the Calc button, below the chart, to select from available options. ## Integral Calculations You can calculate the integral, with respect to x, for a given range of an X-Y plot. Select the applicable integral option using the Calc button. You will be prompted for the x value range over which the calculation is to be performed. The integral represents the area between the curve and the x-axis over the specified range, and the result will be displayed to an estimated number of digits of accuracy. The accuracy will be determined by the number of plotted data points, and where there are few data points and potential accuracy is low, an error range will also be shown with the result, for example: "2.3 +/-0.1". In making this calculation, it is assumed that function plots show smoothly varying trends, whereas this assumption is optional for X-Y data plots (see below). ## Derivative Calculations You can calculate the gradient of an X-Y plot at a given value of x. Select the applicable derivative option using the Calc button. You will be prompted for the x value at which the gradient dy/dx is to be found. The result will be displayed to an estimated number of digits of accuracy. In making this calculation, it is assumed that function plots show smoothly varying trends, whereas this assumption is optional for X-Y data plots (see below). ### Plot dy/dx Tracing The gradient at the plot tracer position is also shown in the trace box beneath the chart. You will see this update as you move the mouse over a plot. This is calculated to the precision allowed by the size of the chart window, and should be treated as an approximate value only. You can use the Calc button to find more accurate results. ## Finding Intersection Points You can find x-axis intercepts for any plot, and points of intersection where two function plots are displayed on the same chart. If there is more than one intersection between the plots, you will be prompted for which point to find. In this case, input "1" for the first point, or "2" for the second etc. The result will be displayed to an estimated number of digits of accuracy. The accuracy will be determined by the number of plotted data points, and where there are few data points and potential accuracy is low, an indication will be shown to signify the approximate nature of the result. Notes. Intersection points are determined using a numerical method which cannot usually find intersection points where the area of intersection is zero. Also note that in making the calculation, it is assumed that function plots show smoothly varying trends, whereas this assumption is optional for X-Y data plots (see below). ## Accuracy and the Smooth Data Assumption When performing calculations with X-Y list data, it will be assumed by default that the data describes a smoothly varying trend. You can, however, turn on or off this setting from the Calc button. This setting will affect the results and accuracy of integral and derivative calculations. Consider the chart below, which shows an X-Y data plot of only a few points. Here we can see that the area beneath the trapezium is calculated to be 2.3. However, we may have initially expected the result to be precisely 2.0, i.e. the area of the trapezium (1 + 3) × 1/2 = 2.0. In effect, what has been calculated is an estimate for the area of a curve passing through the points, rather than a trapezium. The error value "+/-0.1" shown is an indication that there are insufficient points to fix the curve accurately. If you are displaying X-Y list data, you can turn off this assumption setting from the Calc button in the lower part of the Chart Window (uncheck "Assume Smooth Data"). Re-calculating the above result in this case, will yield a value of 2.0, rather than 2.3. Calculations using the Function Graph always assume that the underlying trend is smooth. See also: Graphing a Function, and Graphing Examples. |