Note that the Student VectorCalculus package has commands for returning the Curvature and the RadiusOfCurvature of the osculating circle.

The Space Curves tutor draws and/or animates the osculating circle for a space curve. (You can trick the tutor into drawing it for a plane curve by giving zero as the third component of the vector defining the curve.)

@rlopez 

Sorry about that typo - I tend to use q when naming expressions. As I experimented with the expression f, I named it q in my worksheet and simply copied and pasted without looking carefully enough.

@rlopez 

Sorry about that typo - I tend to use q when naming expressions. As I experimented with the expression f, I named it q in my worksheet and simply copied and pasted without looking carefully enough.

@leaky 

If f = sqrt(2*x+2)/(x+1), then 1/rationalize(1/f) returns 2/sqrt(2*x+2) and no obvious manipulation in Maple "cancels" the 2s.

For this f, the following gets the desired sqrt(2)/sqrt(x+1)

simplify(sqrt(simplify(1/rationalize(1/q^2)))) assuming x>-1

Hence, the title "Conditional approach" where squaring and then taking the square root will generally present sign issues for most expressions.

@leaky 

If f = sqrt(2*x+2)/(x+1), then 1/rationalize(1/f) returns 2/sqrt(2*x+2) and no obvious manipulation in Maple "cancels" the 2s.

For this f, the following gets the desired sqrt(2)/sqrt(x+1)

simplify(sqrt(simplify(1/rationalize(1/q^2)))) assuming x>-1

Hence, the title "Conditional approach" where squaring and then taking the square root will generally present sign issues for most expressions.

@Markiyan Hirnyk Typing sqrt((x+1)/2) and pressing the Enter key results in the "somewhat different expression" that the rationalize command produces. It's a result of Maple's automatic "simplification" rules. There's no simple way to get the expression in the form of the square root of the fraction.

@Markiyan Hirnyk Typing sqrt((x+1)/2) and pressing the Enter key results in the "somewhat different expression" that the rationalize command produces. It's a result of Maple's automatic "simplification" rules. There's no simple way to get the expression in the form of the square root of the fraction.

If you type in sqrt((x+1)/2), and press the Enter key, Maple will automatically "simplify" the expression to what you get when rationalize is applied to (x+1)/sqrt(2*x+2).

There's nothing simple you can do to get Maple to output the expression in a different form.

I think Maplesoft should take a look at the sliders in GeoGebra, that free software that people are using to create apps that don't need some underlying software to run.

In GeoGebra, sliders are one size, and relatively small. All that's there is a line and a disk sliding on the line. No numbers along the line. The only number visible is the value of the slider corresponding to the position of the disk. This permits all kinds of labeling generated by the slider, but removes the problem of providing space for displaying all the value-labels. I've seen this in demos at conferences, and find this approach to sliders most satisfactory.

RJL Maplesoft

Doug pointed this out to me privately by email, and I immediately modified the graph by adding a view option to the plot command. As soon as the original file is replaced with the modified one, downloads will not have this "glitch" in the graph.

I raised Doug's point with our graphics people. Apparently, I've already hit on the best cure by adding the view option.

RJL Maplesoft

To get multiple lines of input to reside in a single execution group, terminate the line with Shift+Enter.

Of course, if the code for the loop has been typed already and resides in separate execution groups, then follow van der Meer's advice and use the Edit menu to join execution groups.

RJL Maplesoft

To get multiple lines of input to reside in a single execution group, terminate the line with Shift+Enter.

Of course, if the code for the loop has been typed already and resides in separate execution groups, then follow van der Meer's advice and use the Edit menu to join execution groups.

RJL Maplesoft

@gdorsch Look up the try/catch mechanism. It will let you branch upon detection of specific errors, or upon detection of any error.

@gdorsch Look up the try/catch mechanism. It will let you branch upon detection of specific errors, or upon detection of any error.

@mzh 

The first part of the demo shows how to obtain the solution via a task template. The second part shows how to obtain the solution from first principles. I just reviewed both parts. The second part, the solution from first principles, is a pretty thorough explanation of how to obtain the solution. It clearly shows why there are two integrals, and how these two integrals are to be obtained.