If it is not already on your hard drive, you will need to download the free DPGraph Viewer to view some of the pictures linked to on this page.

QuickTime free download.

Click here to go to sample problems for Exam IV.

	Take-Home Final Exam (optional)
	Graphing Grids for rectangular and polar graphs
	At this site you can find some java tools that include graphers.  Click on java tools at the bottom of the table of contents on the left.
	Hotmath  You can look at free solutions to problems in exercise sets from a wide variety of mathematics textbooks including Calculus by Larson, Hostetler, Edwards, eighth edition.  They now have chapters 1 - 12 available.  Only a few solutions are still free.
	WIMS  A really nice set of graphing tools by XIAO Gang which will produce pictures and graphs that can be saved.  Included is a free online sequence and series grapher.  Click on Sequence plot at the bottom of the page.  Click on Sigma to compute finite and infinite series sums.  Traces Animes at the same site is a terrific 2D and 3D plotter.
	Here is a page of examples and demonstrations illustrating the formation of a conic section as the intersection of a plane and a cone.

10.1  You need to be able to put the equations of the conics (circles, parabolas, ellipses, and hyperbolas) in standard form.  From standard form you should be able to find the center and radius of a circle, vertex, focus, and equation of directrix of a parabola, center and foci of an ellipse, and center, foci, and equations of the asymptotes of a hyperbola.  Know the reflective property of a parabola and the reflective property of an ellipse.  One use of calculus relating to surfaces involves showing that essentially parallel rays of light striking a parabolic surface are directed through the focus (or rays of light emanating from the focus will be parallel after reflecting off the parabolic reflector).  For EXTRA CREDIT use Theorem 10.2, Reflective Property of a Parabola, on page 696 in your text to prove this.  Follow this link to learn more about liquid mirror telescopes.  They use this property of parabolic reflectors.

10.2  You need to be able to represent a variety of curves (including the conics) parametrically.  Here is a Visual Calculus tutorial on representing curves parametrically.  Here is an animation of the drawing of a cycloid (using flash).  This Quicktime movie by Bruce Simmons demonstrates the Tautochrone Problem (see page 715).

10.3  You need to be able to find dy/dx in a case where a curve is given parametrically by x = f(t) and y = g(t).  You need to be able to find arc length for a curve given parametrically (Theorem 10.8, P722) and area of a surface of revolution where the curve involved in given parametrically (Theorem 10.9, P724).

10.4  You need to be able to represent a variety of curves in polar form and be able to translate back and forth between polar and rectangular form.  You need to be able to find dy/dx as in Theorem 10.11, P733, and be able to find horizontal and vertical tangents.  Here is a Visual Calculus tutorial on polar coordinates.  This link is to a Derive presentation of four graphs of polar equations representing conics and this one shows the effect of changing the eccentricity in the polar equation of an ellipse.  Here is an applet that is a polar grapher.

To the left is the polar graph of   r = 2 + 4sin(2t) - 4cos(2t).   Click the graph to see an animation.

10.5  You need to be able to find area, arc length, and area of a surface of revolution for curves and regions described in polar form.

10.6  You will need to be able to recognize polar equations of conics and be able to translate the polar equation into an equation in rectangular form.

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        Lane Vosbury, Mathematics, Seminole State College   email:  vosburyl@seminolestate.edu

        This page was last updated on 08/21/14          Copyright 2002          webstats