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General Information
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For Students
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For Instructors
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Miscellaneous
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Functions
- New Functions from Old
- Self Test 1 (Quiz on Transformation of Functions) : Determine the relationship between two graphs where one is f(x) and the other is A*f(x) or f(A*x), or f(x)+B, or f(x+B) etc. Comes with instant checking.
- Applet 1 (Stretching and Compression of a Function) : Look at the graph of A*f(B*x) and observe the effects of changing A and B.
- Applet 2 (Translation of a Function) : Look at the graph of A+f(B+x) and observe the effects of changing A and B.
- Applet 3 (New Functions from Old) : Make new functions from old ones by reflecting, translating and stretching.
- Applet 4 (New Functions from Old Game) : For a function out of a list, there is a proposed target function that can be obtained by performing a sequence of transformations on the given function. In each example you have to find such a sequence of transformations that make the graphs coincide.
- Inverse of Functions
Limits
- Limit Laws
- Continuity
- Self Test 3 (Quiz I on Continuous Functions) : Use the definition of continuity to determine if a function is continuous or not. Comes with instant checking.
- Self Test 4 (Quiz on Properties of Continuous Functions)
Derivatives
- Definition of Derivatives
- Trigonometric Derivatives
- Velocity
- Applet 7 (Average Velocity) : Galileo experimented with falling objects. By meas-uring the distance fallen as a function of time he was able to conclude that the velocity is a linear function and that the acceleration is constant. This applet mir-rors his experiments.
- Curve Sketching
- Applet 8 (Behaviour of f, f' and f'' at given points) : Viewing a graph, determine information about a function and its first and second derivative.
- Self Test 8 (Quiz I on the behaviour of f, f' and f'' at given points) : This is a quiz to test your ability to use concepts of differentiablity to infer information about the graph of a function. Comes with instant checking.
- Self Test 9 (Quiz II on the behaviour of f, f' and f'' at given points) : You are given the graphs of f, f' and f'' and you have to determine which is which. Comes with instant checking.
Applications of Derivatives
- Tangent and Secant Lines
- Mean Value Theorem
- Linear Approximations
- Applet 11 (Linear Approximation using the First Derivative)
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