082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

70 Chapter 2 Engineering functions
14 Piecewise continuous; discontinuity att = 2. See
FigureS.2.
f
2
1
16 Discontinuitiesatt = 0,2.See FigureS.4.
g
1
–1 0 1 2 3 t
FigureS.2
15 See FigureS.3.
h
2
1
–1 0 1 2 3 4
FigureS.4
t
0 1 2 3 4 5 6
t
FigureS.3
2.4 REVIEWOFSOMECOMMONENGINEERINGFUNCTIONS
ANDTECHNIQUES
This section provides a catalogue of the more common engineering functions. The important
properties and definitions are included together with some techniques. It is intendedthatreaderswillrefertothissectionforrevisionpurposesandastheneedarises
throughout the rest of the book.
2.4.1 Polynomialfunctions
Apolynomial expressionhas the form
a n
x n +a n−1
x n−1 +a n−2
x n−2 +···+a 2
x 2 +a 1
x+a 0
wherenis a non-negative integer,a n
,a n−1
,...,a 1
,a 0
are constants andxis a variable.Apolynomial
function,P(x), has the form
P(x) =a n
x n +a n−1
x n−1 +a n−2
x n−2 + ··· +a 2
x 2 +a 1
x +a 0
(2.3)
Examples of polynomial functions include
P 1
(x)=3x 2 −x+2 (2.4)
P 2
(z) =7z 4 +z 2 −1 (2.5)
P 3
(t) =3t +9 (2.6)
P 4
(t) =6 (2.7)