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

84 Chapter 2 Engineering functions
I
–I s V
Figure2.31
Atypical diode characteristic.
EXERCISES2.4.3
1 Simplify
(a)
(c)
(e)
e 2x
3e 3x
e x (e x +e 2x )
e 2x
(e 2t ) 3 (e 3t ) 4
e 10t
(b) e2t−3
e 2
(d) e−3 e −7
e 6 e −2
2 Consider theRC circuitofFigure2.29.Given an
initialcapacitor voltageof10Vplotthe variation in
capacitor voltage with time, usingthe same axes, for
the followingpairs ofcomponentvalues:
(a) R=1,C=1µF
(b) R=10,C=1µF
(c) R=3.3,C=1µF
(d) R=56,C=0.1µF
Calculate the time constant, τ,in eachcase.
3 Sketch the following functions,usingthe same axes:
y=e 2x y=e x/2 y=e −2x
for −3x3
4 Sketch agraph ofthe functiony = 1 −e −x for
x0.
Solutions
1 (a) e−x (b) e 2t−5 (c) 1 +e x 2 (a) 10 −6 (b) 10 −5 (c) 3.3 ×10 −6
3
(d) e −14 (e) e 8t (d) 5.6 ×10 −6
TechnicalComputingExercises2.4.3
1 Ploty = e kx fork = −3, −2, −1, 0, 1, 2, 3, for
−3x3.
2 Ploty =ke x fork = −3, −2, −1, 0, 1, 2, 3, for
−3x3.
3 Ploty=5−x 2 andy=e x for−3x3.Forwhich
valuesofxise x <5−x 2 ?
4 Ploty =x 4 andy = e x for −1 x9.Forwhich
valuesofxis(a)e x <x 4 ,(b)e x >x 4 ?