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||             Electronic Proceedings of the Tenth Annual             ||
||  International Conference on Technology in Collegiate Mathematics  ||
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CONTRIBUTED PAPER: 10-C8

Hard Calculus Problems Made Easy by the TI-92 Calculator

David F. Appleyard
Department of Mathematics and Computer Science
Carleton College
One North College Street
Northfield, MN 55057-4025
Phone:  (507)-646-4450
FAX:    (507)-646-4312
E-mail: dappleya@mathcs.carleton.edu

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.