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

2.4 Review of some common engineering functions and techniques 77
weseethefunctionhaspolesatx = 1andx = −2;thatis,thereareverticalasymptotes
atx = 1 andx = −2. Substitution into the function of a number of values ofxallows a
table tobe drawn up:
x −3 −2.5 −2.1 −1.9 −1.5 −1 0 0.5 0.9 1.1 1.5 2 3
y −0.75 −1.43 −6.77 6.55 1.20 0.50 0 −0.40 −3.10 3.55 0.86 0.50 0.30
The graph of the function can then be sketched as shown inFigure 2.23.
y
–2
1 x
Figure2.23
x
Thefunction:y =
x 2 +x−2 .
Engineeringapplication2.7
Equivalentresistance
RecallfromEngineeringapplication1.2thattheformulafortheequivalentresistance
oftwo resistors inparallel isgiven by:
1
R E
= 1 R 1
+ 1 R 2
Consider a circuit consisting of two resistors in parallel as shown in Figure 2.24.
Onehasaknown resistanceof1andtheother hasavariableresistance,R.The
equivalent resistance,R E
, satisfies
Hence,
1
= 1 R E
R + 1 1 = 1 +R
R
R E
=
R
1 +R
Thus the equivalent resistance is a rational function of R, with domain R 0.
The graph of this function is shown in Figure 2.25. When R = 0 we note
that R E
= 0, corresponding to a short circuit. As the value of R increases, that
isR → ∞,theequivalentresistanceR E
approaches1sothatR E
= 1isanasymptote.
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