Answers to the Exercises - 3D Math Primer for Graphics and Game Development - page 782

x(1)−x(0)
1−0

= 1−0
1

3. (a) = 1

x(2)−x(1)
2−1

= 0−1
1

(b) = −1

x(2)−x(0)
2−0

= 0−0
2

(c) = 0

x(6.5)−x(5.5)
6.5−5.5

= 1−(−1)
1

(d) = 2

x(9)−x(0)
9−0

= (−2)−0
9

= − 2
9

(e)

<
:

2−2t 0 < t < 2

0 2 < t < 4

4. v(t) =

π cos(πt) 4 < t < 7

−1 7 < t

5. (a) v(0.1) = 2−2(0.1) = 1.8

(b) v(1.0) = 2−2(1.0) = 0.0

(c) v(1.9) = 2−2(1.9) = −1.8

(d) v(4.1) = π cos(4.1π) = 2.988

(e) v(5) = π cos(5π) = −π

(f) v(6.5) = π cos(6.5π) = 0

(g) v(8) = −1

(h) v(9) = −1

<
:

−2 0 < t < 2

0 2 < t < 4

6. a(t) =

−π 2 sin(πt)

4 < t < 7

0 7 < t

7. (a) a(0.1) = −2

(b) a(1.0) = −2

(c) a(1.9) = −2
(d) a(4.1) = −π 2 sin(4.1π) = −3.050
(e) a(5) = −π 2 sin(5π) = 0

(f) a(6.5) = −π sin(6.5π) = −9.870

(g) a(8) = 0

(h) a(9) = 0