**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