Fplot ('function',limits) plots 'function' between the limits specified by limits. Limits is a vector specifying the x -axis limits (xmin xmax), or the x - and y -axis limits, (xmin xmax ymin ymax). First, plot a line. X = linspace (0,10); y = sin (x); plot (x,y) Set the y -axis limits mode to manual so that the limits to not change. Use hold on to add a second plot to the axes. Ylim manual hold on y2 = 2.sin (x); plot (x,y2) hold off. The y -axis limits do not update to incorporate the new plot.

Limits

The fundamental idea in calculus is to make calculations onfunctions as a variable “gets close to” or approachesa certain value. Recall that the definition of the derivative is givenby a limit

With plot you have to manually define the x values and compute the corresponding y given by the function. x = 0.01:1; y = sin(10.x); plot(x,y,'.-') With fplot you define the function generically, for example as an anonymous function; pass a handle to that function; and let Matlab choose the x values and compute the y values.

provided this limit exists. Symbolic Math Toolbox™ softwareenables you to calculate the limits of functions directly. The commands

which return

and

which returns

illustrate two of the most important limits in mathematics:the derivative (in this case of cos(x))and the exponential function.

One-Sided Limits

You can also calculate one-sided limits with Symbolic Math Toolbox software. For example, you can calculate the limit of x/ x , whose graph is shown in the following figure, as x approaches 0 from the left or from the right.

To calculate the limit as x approaches 0 from the left,

Matplotlib Plot Limits

enter

To calculate the limit as x approaches 0 from the right,

enter

Since the limit from the left does not equal the limit fromthe right, the two- sided limit does not exist. In the case of undefinedlimits, MATLAB^® returns NaN (not a number).For example,

returns

Fplot Y Axis Limits

Observe that the default case, limit(f) is the same as limit(f,x,0). Explore the options for the limit command in this table, where f is a function of the symbolic object x.

Fplot Limits