# Tag: Calculus

1. ### 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.
2. ### 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.
3. ### Convergence and continuity of a function

This applet illustrates the ε-δ 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.
4. ### Differentiability of a function

This applet illustrates the definition of derivative as the limit of the gradient of a chord.
5. ### Convergence of a sequence

This applet illustrates the ε-M definition of convergence of a sequence.
6. ### Riemann sums and partitions

This applet illustrates upper and lower Riemann sums and refinement of partitions.
7. ### 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.
8. ### 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.
9. ### Parametric curves

This applet plots and traces a parametric curve, given as a vector function in R2.
10. ### Two parametric curves

This applet plots two parametric curves simultaneously. It can be used to explore whether two particles collide.

Number of posts found: 18