### 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.