Section 8.1
Chapter 8 Functions of Several
Variables
5. (a) g (0, 0, 0) = e 0+0+0 = 1
(b) g (1, 0, 0) = e1+0+0 = e
(c) g (0, 1, 0) = e0+1+0 = e
(d) g (z, x, y) = ez+x+y = ex+y+z
(e) g (x + h, y + k, z + l) = ex+h+y+k+z+l
8.1 Functions of Several Variables
Section 7.1
4.
Chapter 7 Further Integration
Techniques and Applications of
the Integral
+
+
I
ex

2
ex
5.
+
D
x 1

2x
1
2
e2x
+
2
1
4
e2x

0
1 e2x
8
2.
+

I
e x
3
e
x
I
e2x
2
(x2  1)e 2x dx
x
+ 0
e
3xex dx = 3xex  3ex + C
ex
= (2  x)ex +
Section 6.1
Chapter 6 The Integral
9 . ( 1 + x ) d x =1 d x + x d x
6.1 The Indefinite Integral
x2
=x+ 2 +C
n+1
x
1 . xn d x = n + 1 + C; n = 5
1 0. ( 4  x ) d x = 4 d x  x d x
6
x5 dx = x + C
6
x2
= 4x  2 + C
n+1
x
2 . xn d x = n + 1 + C; n = 7
xn+1
1
Section 5.1
f'(x) is defined for all x in [0, 3]. Thus, we have
the stationary point at x = 2 and the endpoints x
= 0 and x = 3 :
x
0
2
3
f(x) 1
3
2
The graph must decrease from x = 0 until x = 2 ,
then increase again until x = 3 .
Chapter 5 Further App
Section 1.1
6. From the graph, we find
(a) f(1) = 20
(b) f(2) = 10
Chapter 1 Functions and Linear
Models
y
1.1 Functions from the Numerical,
Algebraic, and Graphical
Viewpoints
20
1. Using the table,
(a) f(0) = 2
(b) f(2) = 0.5.
10
x
2. Using the table,
(