Sage Demos for Calculus

Limits: This demo attempts to compute left, right, and double sided limits while providing numerical support and a plot. [Limits sandbox]
Related Desmos Definition of Limit Demo
Average Rates of Change: This demo compute average rates of change for a given function (defined by formula or table). The demo also provides a plot to help visualize what is being computed.
Definition of the Derivative: This demo plots secant lines and tangent lines. It also computes difference quotients and derivatives. This allows the user to explore the limit definition of the derivative. [Derivatives Sandbox]
Related Desmos Definition of the Derivative Demo
Tangent Lines: This demo plots a function along with a tangent line based at a point determined by a slide bar. Derivative information and the equation of the tangent line are also displayed. If a box is checked, the quadratic approximation (i.e. second order Taylor polynomial) is also computed and displayed.
Related Desmos Tangent Line Demo
Derivatives Graphs: This demo plots a function and its first and second derivatives along with points based at $x=a$ on these graphs (this point is determined by a slider). Using the derivative values, it is determined whether the function is increasing, decreasing, or has a critical point and whether it is concave up, concave down, or possibly has an inflection point.
Related Desmos Graphs of Derivatives Demo
Derivatives Practice: This is a Sage enabled version of a derivatives practice worksheet. The demo computes and prints the derivatives of a given function up to a specified order.
Taylor Polynomials: This demo computes and graphs Taylor polynomials. There is an option whether to show a single polynomial, all polynomials up to a specified order, or animate a sequence of polynomials.
Newton's Method: This demo computes roots using Newton's method. It also provides an animated visualization of the method by providing graphs of tangents.
Critical Points: This demo computes critical points and solutions of $f''(x)=0$. These points are plotted and classified (i.e. local min, local max, neither and inflection point or not).
Optimization: This demo computes the minimum and maximum value of a function $f(x)$ when $a \leq x \leq b$. The demo also includes a plot of the function and highlights the critical points and end points.
Area Approximation: This demo computes left, right, midpoint, trapezoid, and Simpson's rule approximations of $\int_a^b f(x)\,dx$. The demo also produces a plot to show what is being computed.

Area Approximation II: The demo computes left, right, and trapezoid rule approximations of $\int_a^b f(x)\,dx$. The demo also produces a plot to show what is being computed. Note: This demo allows for general partitions (not just equally spaced) and it also allows one to specify a function using a table of values.