Calculus
Table of Contents
- Limits and Their Properties
- Review of Transformations
- Review of Transformations 2
- Differentiation
- Application of Differentiation
- Integration
- Logarithmic, Exponential and other Transcendental Functions
- Applications of Integration
- Solid of Revolution
- Integration Techniques, L'Hopital's Rule and Improper Integrals
- Visual Limits (L'Hopital's)
- Visual Limits (L'Hopital's) 2
- Visual Limits (L'Hopital's) 3
- Visual Limits (L'Hopital's) 4
- Visual Limits (L'Hopital's) 5
Review of Transformations
|
Use the sliders to review transformations. |
|
|
|
In general, if the base function is y=f(x) (where k>0), then describe each transformation. 1) y=f(x)+k 2) y=f(x)-k 3) y=f(x+k) 4) y=f(x-k) 5) y=-f(x) 6) y=f(-x) 7) y=-f(-x) |
Solid of Revolution
Creatung a solid through rotation of a graph round the x- or y-axis.[br][br][b]Exercise[/b][br]Visualize the solid of revolution which is determined by the rotation of the sine function between 0 and 2π.
Andreas Lindner
Visual Limits (L'Hopital's)
|
[math] \textbf{(a) Describe the type of indeterminate form (if any) that is obtained by direct substitution.}\\ \textbf{(b) Evaluate the limit using L'Hopital's Rule if necessary.}\\ \textbf{(c) Using the applet explain how the graph verifies you results.}\\ \displaystyle \large \begin{equation} \lim_{x\to 0^+} (-x \ln(x)) \end{equation} [/math] |
|
|