HP 15c Collector's Edition User Manual

Appendix E: A Detailed Look at f 251
Since you’re evaluating this integral numerically, you might think (naively
in this case, as you’ll see) that you should represent the upper limit of
integration by 10
99
—which is virtually the largest number you can key
into the calculator. Try it and see what happens.
Key in a subroutine that evaluates the function f(x) = xe
−x
.
Keystrokes
Display
| ¥
000-
Program mode.
´ b 1
001-42,21, 1
”
002- 16
'
003- 12
*
004- 20
| n
005- 43 32
Set the calculator to Run mode. Then set the display format to i 3 and
key the limits of integration into the X- and Y-registers.
Keystrokes
Display
| ¥ Run mode.
´ i 3 Sets display format to i 3.
0 v
0.000 00
Keys lower limit into Y-register.
“ 99
1 99
Keys upper limit into X-register.
´ f 1
0.000 00
Approximation of integral.
The answer returned by the calculator is clearly incorrect, since the actual
integral of f(x) = xe
−x
from 0 to ∞ is exactly 1. But the problem is not that
you represented ∞ by 10
99
, since the actual integral of this function from
0 to 10
99
is very close to 1. The reason you got an incorrect answer
becomes apparent if you look at the graph of f (x) over the interval of
integration:

HP 15c Collector's Edition Specifications

General

Model	HP 15c Collector's Edition
Category	Calculator
Type	Scientific
Power Source	Battery
Manufacturer	HP
Display	LCD
Functions	complex numbers, matrix operations

Summary

Introduction

This Handbook

Outlines the structure of the manual, detailing its parts and how to use it for learning.

The HP Community

Discusses user groups and websites for HP calculator enthusiasts and information sharing.

Part I: HP 15c Fundamentals

Section 1: Getting Started

Covers basic operations like powering on, keyboard layout, and primary/alternate functions.

Section 2: Numeric Functions

Explains essential numeric operations including logs, trig, powers, and conversions.

Section 3: The Automatic Memory Stack, LAST X, and Data Storage

Details the RPN stack, LAST X register, and data storage operations.

Part II: HP 15c Programming

Section 6: Programming Basics

Introduces core programming concepts: creating, loading, running programs, and memory.

Section 8: Program Branching and Controls

Covers controlling program flow using branching, loops, and conditional tests.

Part III: HP 15c Advanced Functions

Section 11: Calculating With Complex Numbers

Covers entering, manipulating, and performing calculations with complex numbers.

Section 12: Calculating With Matrices

Explains matrix operations, including dimensioning, element access, and calculations.

Section 13: Finding the Roots of an Equation

Details using the SOLVE function for numerical root finding and equation solving.

Section 14: Numerical Integration

Explains how to perform numerical integration using the ∫f(x)dx key and subroutines.

Appendix A: Error Conditions

Error 8: No Root

Explains the error when the SOLVE function cannot find a root.

Error 0: Improper Mathematics Operation

Lists and explains errors related to mathematical operations and illegal arguments.

Appendix D: A Detailed Look at SOLVE

How SOLVE Works

Explains the numerical technique and logic behind the SOLVE algorithm.

Finding Several Roots

Discusses methods for finding multiple roots of an equation using the SOLVE function.