Online Applications

Sect. 2.1: Secant Lines Approaching Tangent Lines  The red line is a tangent line fixed at some point.  Watch how the secant line "approaches" the tangent line as you drag the green point closer the red point along the function (the x-coordinate of the green point is approaching the x-coordinate of the red point of tangency).

Sect. 2.2: Limits This applet may help you visualize the difference between left-limits, right-limits, and overall limits, particularly with piecewise functions.  Play around with it, but do not become dependent on this to calculate limits for you!

Sect. 2.8: Sketching the graph of a derivative f '(x) given f(x) This applet can help you visualize the slopes of f(x) and how this determines the shape of f '(x).  You can even do a rough sketch of what you think f '(x) will look like and compare it to the answer.

Sect. 3.9: Various Related Rates Animations

Ladder leaning against a wall and sliding downward (Top sliding down at a constant rate)

Boat being pulled toward a dock at a constant rate

Inverted cone being filled at a constant rate

Man walking towards a lamppost at a constant rate

Fish being reeled in at a constant rate

A circle with area growing at a constant rate

A lighthouse with a beam rotating at a constant rate

A triangular water trough filled at a constant rate

These animations can be found at the site: http://www2.seminolestate.edu/lvosbury/calculusI_folder/RelatedRateProblems.htm