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