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

2.4 Review of some common engineering functions and techniques 79
5 Showthat
I(x) = 2x
3 − 7 9 + 23
9(3x +2)
can be expressed in the equivalent form
2x 2 −x+1
3x+2
Sketch the rational functionI(x)and state any
asymptotes.
6 Showthat
p(x) =2x + 1 2 + 9
2(2x +3)
can be writtenin the equivalent form
4x 2 +7x+6
2x+3
Sketch the rational function p(x)and stateany
asymptotes.
7 Show thatthe function
y(x)=x+ 7 −x
x 2 +3
can be expressed in the equivalent form
x 3 +2x+7
x 2 +3
Sketch the rational functiony(x) andstate any
asymptotes.
Solutions
1 (a) 2 (b) −7 (c) − 3 2
(d) −2,2 (e) −5, −1 (f) −6,3
(g) −1,0,1
(h) −5
2 (a)y=6 (b)h=−1
(c)y=3 (d) v=1
(e)r= 2 3
(f)a=1
4 (a) y=x+3 (b) y=2x−1
(c)y= x 2 − 3 4
(e) y=2x−1
(g) y=4−2x
5 x=− 2 2x
,I =
3 3 − 7 9
(d) y=3x−1
(f) y=3x−2
6 x=− 3 2 ,p=2x+1 2
(g)m=− 3 2
3 (a)x=2 (b)t=−1
(c) s=−2,1 (d) t =−1,1
(e) s=−1,1 (f) x=−1,1
(g) f =−3,2 (h) t =−3
(i) x=0.5 (j) r=−3,4
7 y=x
TechnicalComputingExercises2.4.2
1 Useatechnicalcomputing languageto plotthe
followingrational functions.Stateany asymptotes.
(2x +1)
(a) f(x) = −4x4
(x−3)
s
(b) g(s) = −3s3
(s+1)
z
(c) h(z) =
(z 2 −3z3
+1)
(d) y(x) = (x+1) −3x3
x
2x
(e) r(x) =
−3x3
(x −1)(x −2)
2 Plotthe functionsgiven in Question4in
Exercises2.4.2 for −10 x10.