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

78 Chapter 2 Engineering functions
R E
1
R
1 V
R E
R
Figure2.24
Two resistorsin parallel.
Figure2.25
Theequivalent resistance,R E ,
increases asRincreases.
EXERCISES2.4.2
1 State the poles ofthe followingrational functions:
(a) y(x) = x +3
x −2
(c) y(t) = t2 +t+1
2t+3
3
(e) H(s) =
s 2 +6s+5
2s+7
(f) G(s) =
s 2 +3s−18
(g) x(t) = 9
t 3 −t
2t−6
(h) p(t) =
t 2 +10t+25
(b) y(x) = 2x+1
x +7
(d) X(s) = s +1
s 2 −4
2 Describethe horizontalasymptote ofeachofthe
following functions:
(a) y(x) =6+ 1 x
(c) y(r) =3− 2 5r
(e) r(v) = 2v−5
3v
(f) a(t) = t2 +2t+1
t 2
(g) m(s) = 10−2s−3s2
2s 2
(b) h(t) = 2 t −1
(d) v(t) = 6 +t
t
3 Describethe vertical asymptotes ofeachofthe
following functions:
(a) y(x) = 3x+1
x −2
(c) h(s) =
9
(s +2)(s −1)
(b) y(t) = 6t−3
4t+4
(d) G(t) = 1
t 2 −1
(f) y(x) =
(g) w(f)=
2x
x 2 −1
f +2
f 2 +f−6
(h) P(t) = t2 +t+1
t 2 +6t+9
(i) T(x) =
(j) Q(r) =
x3
2x−1
6 +r
r 2 −r−12
(e) H(s) =
s
s 2 −1
4 Describethe obliqueasymptote ofeachofthe
following functions:
(a) y(x)=x+3+ 1
x −1
(b) y(x)=2x−1+ 3
x +2
(c) y(x) = x 2 − 3 4 + 1
2x+7
(d) y(x)=3x−1+ 5
2x+2
(e) y(x)=2x−1+ x +2
x 2 −1
(f) y(x)=3x−2+ 4
2x−1
(g) y(x)=4−2x+ 3
2x+3