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

104 Chapter 2 Engineering functions
6 Expressacoshx +bsinhx,whereaandbare
constants,in terms ofe x and e −x .
7 Show that the pointx = coshu,y = sinhulies onthe
curve
x 2 −y 2 =1
8 Provethehyperbolicidentitieslistedintheboxearlier
in thissection.
Solutions
1 (a) 10.0179 (b) 2.5775 (c) 0.7398
(d) 0.6481 (e) 0.2757 (f) 1.1048
(g) 10.0677 (h) −0.4210 (i) −3.6269
(j) −1.0091 (k) −0.8854 (l) 0.8868
2 (a) 1.8184 (b) 1.3170 (c) −0.2554
3 (a) 11coshx +sinhx (b) cosh2x +7sinh2x
(c) −3cosh3x −7sinh3x
4 (a) 3.5e x −0.5e −x
(b) e 2x −2e −2x
(c) 1.25e 3x +1.75e −3x
5 (a+b)coshx+(a−b)sinhx
6
a +b
2 ex + a −b
2 e−x
TechnicalComputingExercises2.4.5
1 Useatechnicalcomputing language to draw
(a)y = sinhx (b)y = coshx
(c)y=tanhxfor−5x5.
2 Draw graphs ofy = sinhx,y = coshx andy = ex
2 for
0 x5. What happens to the threegraphs asx
increases? Canyou explain thisalgebraically?
3 Draw
(a) y=sinh −1 x
(b) y=cosh −1 x
(c) y=tanh −1 x
−5x5
1x5
−1<x<1
2.4.6 Themodulusfunction
Themodulusofapositivenumberissimplythenumberitself.Themodulusofanegative
number is a positive number of the same magnitude. For example, the modulus of 3 is
3; the modulus of −3 is also 3. We enclose the number in vertical lines to show we are
findingits modulus,thus
|3|=3 |−3|=3
Mathematically wedefinethe modulusfunctionasfollows:
The modulus
{
functionisdefinedby
x x0
f(x)=|x|=
−x x<0
Figure2.38illustratesagraphof f (x) = |x|.Themodulusofaquantityisnevernegative.
Consider two points on thexaxis,aandb, asshown inFigure 2.39. Then
|a −b| = |b −a| = distancefromatob