Tag: Calculus

Exploring areas with hyperbolic and trigonometric functions
This applet explores a geometric interpretation of the parameter t in the parameterisation of the standard hyperbola using cosh and sinh.melbapplets.ms.unimelb.edu.au/2023/02/01/exploringareaswithhyperbolicandtrigonometricfunctions

Tangency: chords, tangents and velocity of a parametric curve
This applet explores the velocity vector of a parametric curve, and its relationship to the chord r(t+h)r(t) and the difference quotient.melbapplets.ms.unimelb.edu.au/2021/08/19/tangencychordstangentsandvelocityofaparametriccurve

Convergence and continuity of a function
This applet illustrates the εδ definitions of the limit and continuity of a function. It can be used to investigate (non)convergence or (dis)continuity of real functions, including the Dirichlet everywhere discontinuous function and variants.melbapplets.ms.unimelb.edu.au/2021/07/12/convergenceandcontinuityofafunction

Differentiability of a function
This applet illustrates the definition of derivative as the limit of the gradient of a chord.melbapplets.ms.unimelb.edu.au/2021/07/12/differentiabilityofafunction

Convergence of a sequence
This applet illustrates the εM definition of convergence of a sequence.melbapplets.ms.unimelb.edu.au/2021/07/12/convergenceofasequence

Riemann sums and partitions
This applet illustrates upper and lower Riemann sums and refinement of partitions.melbapplets.ms.unimelb.edu.au/2021/07/12/riemannsumsandpartitions

Sequences and series
This applet shows the relationship between terms of a sequence and the partial sums of a series. It also allows exploration of some important sequences & series including geometric and harmonic sequences.melbapplets.ms.unimelb.edu.au/2021/07/09/sequencesandseries

Inverse of a function
This applet shows the construction of the inverse of a function, and can be used to explore whether the inverse is a function.melbapplets.ms.unimelb.edu.au/2021/07/09/inverseofafunction

Parametric curves
This applet plots and traces a parametric curve, given as a vector function in R2. 
Two parametric curves
This applet plots two parametric curves simultaneously. It can be used to explore whether two particles collide.melbapplets.ms.unimelb.edu.au/2021/07/09/twoparametriccurves
Number of posts found: 18