Understanding Engineering Mathematics

− 10

y

y = x +

y^ =

x

(^1) x
1
x
Figure 10.8Sketch ofy=x+
1
x
.
(iii)y=xex
Symmetry:none
Gateways:(0, 0) only
Restrictions:none – defined for all values ofx, and no discontinuities
Asymptotes:Asx→−∞,y→0 from below (i.e. from values less
than zero)
Points:none special except the
Stationary value: which, from Review Question 10.1.3(iii) is a
minimum atx=−1. We also have apointofinflectionatx=− 2
Putting all this together yields the graph shown in Figure 10.9.
y
y = xex
x
− 1 0
Figure 10.9Sketch ofy=xex.
(iv)y=sinxcosx=^12 sin 2x
This is the graph of a standard elementary function, which we already
know from Chapter 6.