Piecewise Defined Functions Evaluate the piecewise defined function at the indicated values. 31. f ( x ) = { x 2 if x < 0 x + 1 if x ≥ 0 f (−2), f (−1) f (0), f (1), f (2)
Piecewise Defined Functions Evaluate the piecewise defined function at the indicated values. 31. f ( x ) = { x 2 if x < 0 x + 1 if x ≥ 0 f (−2), f (−1) f (0), f (1), f (2)
Piecewise Defined Functions Evaluate the piecewise defined function at the indicated values.
31.
f
(
x
)
=
{
x
2
if
x
<
0
x
+
1
if
x
≥
0
f(−2), f(−1) f(0), f(1), f(2)
Definition Definition Group of one or more functions defined at different and non-overlapping domains. The rule of a piecewise function is different for different pieces or portions of the domain.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
Chapter 2 Solutions
Student Solutions Manual for Stewart/Redlin/Watson's Precalculus: Mathematics for Calculus, 7th
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