Electronic Proceedings of the Tenth Annual International Conference on Technology in Collegiate MathematicsChicago, Illinois, November 6-9, 1997Paper C008Hard Calculus Problems Made Easy by the TI-92 Calculator |
David F. AppleyardDepartment of Mathematics and Computer Science Carleton College One North College Street Northfield, MN 55057-4025 USA Phone: (507)-646-4450 Fax: (507)-646-4312 dappleya@mathcs.carleton.edu |
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ABSTRACT
The TI-92 calculator solves quite easily some challenging and/or computationally lengthy problems from a standard first-year calculus course. The topics of these problems are: calculating an exponential limit, finding the extreme values of a function on an interval, analyzing the shape of the graph of a function, finding the area of a triangle formed by a tangent line to a complicated curve and the coordinate axes, doing an antidifferentiation and including an initial condition, finding when the volumes of two solids of revolution are equal, determining which member of a family of curves has a certain length, evaluating an improper integral with a parameter, requiring the partial sums of a series of positive constants to be sufficiently close to the sum of the series, and calculating how well a function on an interval is approximated by one of its Taylor polynomials. The problems and solution techniques come from various Advanced Placement Calculus with Graphing Calculator Workshops the presenter has conducted for secondary school teachers over the last seven years.Keyword(s): calculus, TI-92, integrals, limits, sequences and series