Sequences of real numbers
Consider the sequence [math]f:\mathbb{N}\rightarrow\mathbb{R}[/math] defined by [math]f\left(n\right)=a_n[/math] for [math]n\in\mathbb{N}[/math]. In the following simulation you can plot a finite number of terms of the sequence.[br][br][b]Things to try:[/b][br][list][*]Drag the slider [b]n[/b] to explore the values of [math]a_n[/math].[/*][*]Change the function defining the sequence.[b] [/b][/*][*][b]Example: [/b](-1)^n/(sqrt(n+1))[/*][*][b]Example: [/b]sin(n+1)/(2*n)[/*][/list]
Partial derivatives and Tangent plane
This simulation shows the geometric interpretation of the partial derivatives of [i]f[/i]([i]x,y[/i]) at point A in [math]\mathbb{R}^2[/math]. It also shows the tangent plane at that point.[br][br]Things to try: [list][*]Drag the point A in the xy-plane or type specific values on the boxes. [/*][*]Select the object you want to show: Tangent plane, f[sub]x[/sub] or f[sub]y[/sub]. [/*][*]Use right click and drag the mouse to rotate the 3D view or click on View button.[/*][/list]
Slope fields of ordinary differential equations
Vector properties and basic operations
Basic operations with complex numbers
Instructions:
[list][*]Select an operation (right screen): addition, subtraction, multiplication, division or a linear combination.[br][/*][*]Drag the points to change the complex numbers, or use the input boxes (left screen).[br][/*][*]Enter your answer in cartesian form to show a geometric representation of the result.[/*][/list][br][br]