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

74 Chapter 2 Engineering functions
P(x)
x 1 x 2 x 3 x
Figure2.20
A polynomial function whichcuts
thexaxisat pointsx 1 ,x 2 andx 3 .
EXERCISES2.4.1
1 State the degree ofthe followingpolynomial (c) 3w −5w 2 +12w 4
expressions:
(d) 7x −x 2
(a) z 3 +2z 2 −8+13z
(e) 3(2t 2 −9t +1)
(b) t 2 −5t 5 +2−8t 3 (f) 2z(2z +1)(2z −1)
Solutions
1 (a) 3 (b) 5 (c) 4 (d) 2 (e) 2 (f) 3
TechnicalComputingExercises2.4.1
UseatechnicalcomputinglanguagesuchasMATLAB ® to
dothe following exercises.
1 (a) Ploty =x 3 andy = 4 −2x in the interval
[-3,3].Beaware that in MATLAB ® ,to carry out
operationsonindividual elements ofavector,
special notation is used.Forexample to multiply
each element in vectorabythe corresponding
element in vectorb(having the same dimension
asvectora)you would typea.*b.Other
functionssuch asraisingto apower alsorequire a
dotprefixifthey are to be carried outoneach
individual element, rather than the whole matrix.
Note thexcoordinate ofthe point ofintersection.
(b) Drawy =x 3 +2x −4. Note the coordinate of
the point where the curve cutsthexaxis.
Compare your answer with that from (a).Explain
your findings.
2 Plotthe followingfunctions:
(a) y=3x 3 −x 2 +2x+1
−2x2
(b) y=x 4 + x3
3 − 5x2 +x−1 −3x2
2
(c) y=x 5 −x 2 +2 −2x2
Henceestimatethe real roots of
0=3x 3 −x 2 +2x+1 −2x2
0=x 4 + x3
3 − 5x2
2 +x−1
−3x2
0=x 5 −x 2 +2 −2x2
3 Usetherootsfunctionin MATLAB ® orequivalent
to calculateamore accurate value forthe real roots
estimated in question 2 andconfirm your answers are
correct.
4 (a) Drawy = 2x 2 andy =x 3 +6 usingthe same
axes.Use yourgraphs to findapproximate
solutionstox 3 −2x 2 +6 = 0.
(b) Addthe liney = −3x +5 to yourgraph.State
approximatesolutionsto
(i) x 3 +3x+1=0
(ii)2x 2 +3x−5=0