Single-stepping through differentiation problems

The DiffTutor  routine launches an interactive tutor to walk through the stages of differentiation problems.  While walking through a problem, students can apply a rule, ask for a hint to the problem, display a fill solution, or jump to the final answer all with the simple click of buttons.  If students need further clarification to the particular rules, select the rule from the Rule Definition  menu.  If students already understand specific rules, they can select the specific rule from the Understood Rules  menu.

>	DiffTutor(ln(x)*sin(x));

Single-stepping through integration problems

Interactive tutors are also available for integration and limit problems using the IntTutor and LimitTutor respectively.  The following shows the results after walking through the stages of a problem using indefinite integration.  To walk through the same problem with definite integtraion, simply enter an integral and start over.

>	IntTutor(csch(x));

Learning by seeing in interactive tutors

Numerous tutors also exist for the various visualization routines available in this package.  Not only is the concept conveyed graphically, but the corresponding integrals, numerical approximations, and required syntax to display this image into the Maple worksheet are also available.

Curve Analysis

The CurveAnalysisTutor  launches a tutor interface that analyzes the graph of a function on an interval.

>	CurveAnalysisTutor();

Tangent and Secant

The TangentSecantTutor  command launches an interface that shows how the secant line between  and a point b on the graph of a function approaches a tangent line, as b approaches  .

>	TangentSecantTutor(x^3-2,x=1);

Mean Value Theorem

The MeanValueTheoremTutor  command launches a tutor interface that illustrates the Mean Value Theorem applied to a function on an interval.  Change the interval and see the results.

>	MeanValueTheoremTutor(1/x, x=0.5..2.5);

Approximate Integration

The ApproximateIntTutor  command launches a tutor interface that computes, plots, and animates approximated definte integrals of a function.

>	ApproximateIntTutor(2*x*sin(x), x=0..2*Pi);

Volume of Revolution

The VolumeOfRevolutionTutor  displays the plot, interval, and area of the volume of revolution of a function where the axis of revolution can be either the horizontal or vertical axis.  The corresponding Maple command is displayed in the bottom of the maplet application.  Copy this command from the maplet application and paste the result into a Maple worksheet.

>	VolumeOfRevolutionTutor(sin(x)*x, x=-10..10);

Taylor Approximation

The TaylorApproximationTutor  displays the Taylor Approximation of a function and allows you to animate the approximation.

>	TaylorApproximationTutor(tanh(x));