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Business Calculus problem in Documents, Problem #2 only

Business Calculus problem in Documents, Problem #2 only wont paste correctly

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1)    

i.       Plot over the interval [0, 2], and compute  for n = 5, 10, 100, and 500.

ii.     Use your results from part (i) to guess the exact value of.

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Business Calculus Math 1325

Homework 5

by

Team: _______

We, the undersigned, affirm that each of us participated fully and equally in the completion of this assignment and that the work contained herein is original. Furthermore, we acknowledge that sanctions will be imposed jointly if any part of this work is found to violate the Student Code of Conduct, the Code of Academic Integrity, or the policies and procedures established for this course.

______________________________ ______________________________

Name (printed) Signature

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I expect a lot of detail in your responses to these problems. All work must be explained in complete sentences. If a blank Excel sheet is used, you must show the first five rows, including the titles of each row, and the last 3 rows. Show equations as you typed them in Excel. Show and label all graphs. Graphs must be trimmed so that they show pertinent detail. All indicators used with the macros must be shown. If ever you are not sure if something should be explained or shown, then explain or show it.

1) Create a new Excel file that

i.

Computes , where the function f is given by the following .
ii. Based on this computation, what do you think is the area under the graph of f, above the x-axis and over [-5, 5].
iii. Do you think that it is likely, or unlikely, that f is a probability density function? Justify your answer.

2) Use Midpoint Sums.xls to
i.
Plot over the interval [0, 2], and compute for n = 5, 10, 100, and 500.
ii.
Use your results from part (i) to guess the exact value of.
3) Evaluate the following by using the method in
Example 2
from
E-Text (slide 160-163)
.
(Hint: Use
Integrating.xls only to check your answers)

(i)

(ii)
4)
Use
Integrating.xlsm
to graph and evaluate for t = 1, 5, 10, 20, and 100. Leave the parameter
t as a constant
. Changing t and recomputing the sheet should change the plot and integral correspondingly. What happens to the value of the integral as s increases?

5)
Suppose is the demand function for a certain good of audio speakers.
i. Use Graphing.xls to plot D(q) and estimate the total possible revenue.
ii. Use Integrating.xls to compute the total possible revenue.
iii.
Assuming that, compute the revenue, the consumer surplus, and the lost revenue from units not sold.

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0 0 = 0 0
P2 1

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2 0 = ERROR:#DIV/0! = ERROR:#DIV/0! 2 0 = 0 0
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0 = ERROR:#DIV/0! = ERROR:#DIV/0! 3 0 = 0 0
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0 = ERROR:#DIV/0! = ERROR:#DIV/0! 4 0 = 0 0
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0 = ERROR:#DIV/0! = ERROR:#DIV/0! 5 0 = 0 0
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0 = ERROR:#DIV/0! = ERROR:#DIV/0! 6 0 = 0 0
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0 = ERROR:#DIV/0! = ERROR:#DIV/0! 7 0 = 0 0
8

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 8 0 = 0 0
9

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 9 0 = 0 0
10

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 10 0 = 0 0
11

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 11 0 = 0 0
12

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 12 0 = 0 0
13

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 13 0 = 0 0
Definition Computation Plot Interval 14

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 14 0 = 0 0

Formula for

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0 = ERROR:#DIV/0! = ERROR:#DIV/0! 15 0 = 0 0

= =

16

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 16 0 = 0 0
Number of subintervals (n): 17

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 17 0 = 0 0
Intervals Midpoint Sum 18

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 18 0 = 0 0
n

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0 = ERROR:#DIV/0! = ERROR:#DIV/0! 19 0 = 0 0
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0 = ERROR:#DIV/0! = ERROR:#DIV/0! 20 0 = 0 0
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0 = ERROR:#DIV/0! = ERROR:#DIV/0! 21 0 = 0 0
Constants 22

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 22 0 = 0 0
s

23

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 23 0 = 0 0
t

24

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 24 0 = 0 0
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0 = ERROR:#DIV/0! = ERROR:#DIV/0! 25 0 = 0 0
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26

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 26 0 = 0 0
w 27

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 27 0 = 0 0
28

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 28 0 = 0 0
29

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 29 0 = 0 0
30

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 30 0 = 0 0
31

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 31 0 = 0 0
32

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 32 0 = 0 0
33

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 33 0 = 0 0
34

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 34 0 = 0 0
35

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 35 0 = 0 0
36

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 36 0 = 0 0
37

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 37 0 = 0 0
38

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 38 0 = 0 0
39

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 39 0 = 0 0
40

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 40 0 = 0 0
41

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 41 0 = 0 0
42

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 42 0 = 0 0
43

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 43 0 = 0 0
44

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 44 0 = 0 0
45

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 45 0 = 0 0
46

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 46 0 = 0 0
47

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 47 0 = 0 0
48

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 48 0 = 0 0
49

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 49 0 = 0 0
50

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 50 0 = 0 0
51

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 51 0 = 0 0
52

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 52 0 = 0 0
53

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 53 0 = 0 0
54

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 54 0 = 0 0
55

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 55 0 = 0 0
56

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 56 0 = 0 0
57

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 57 0 = 0 0
58

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 58 0 = 0 0
59

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 59 0 = 0 0
60

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 60 0 = 0 0
61

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 61 0 = 0 0
62

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 62 0 = 0 0
63

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 63 0 = 0 0
64

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 64 0 = 0 0
65

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 65 0 = 0 0
66

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 66 0 = 0 0
67

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 67 0 = 0 0
68

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 68 0 = 0 0
69

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 69 0 = 0 0
70

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 70 0 = 0 0
71

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 71 0 = 0 0
72

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 72 0 = 0 0
73

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 73 0 = 0 0
74

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 74 0 = 0 0
75

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 75 0 = 0 0
76

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 76 0 = 0 0
77

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 77 0 = 0 0
78

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 78 0 = 0 0
79

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 79 0 = 0 0
80

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 80 0 = 0 0
81

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 81 0 = 0 0
82

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 82 0 = 0 0
83

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 83 0 = 0 0
84

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 84 0 = 0 0
85

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 85 0 = 0 0
86

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 86 0 = 0 0
87

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 87 0 = 0 0
88

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 88 0 = 0 0
89

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 89 0 = 0 0
90

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 90 0 = 0 0
91

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 91 0 = 0 0
92

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 92 0 = 0 0
93

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 93 0 = 0 0
94

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 94 0 = 0 0
95

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 95 0 = 0 0
96

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 96 0 = 0 0
97

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 97 0 = 0 0
98

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 98 0 = 0 0
99

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 99 0 = 0 0
100

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 100 0 = 0 0
101

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 101 0 = 0 0
102

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 102 0 = 0 0
103

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 103 0 = 0 0
104

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 104 0 = 0 0
105

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 105 0 = 0 0
106

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 106 0 = 0 0
107

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 107 0 = 0 0
108

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 108 0 = 0 0
109

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 109 0 = 0 0
110

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 110 0 = 0 0
111

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 111 0 = 0 0
112

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 112 0 = 0 0
113

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 113 0 = 0 0
114

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 114 0 = 0 0
115

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 115 0 = 0 0
116

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 116 0 = 0 0
117

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 117 0 = 0 0
118

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 118 0 = 0 0
119

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 119 0 = 0 0
120

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 120 0 = 0 0
121

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 121 0 = 0 0
122

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 122 0 = 0 0
123

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 123 0 = 0 0
124

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 124 0 = 0 0
125

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 125 0 = 0 0
126

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 126 0 = 0 0
127

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 127 0 = 0 0
128

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 128 0 = 0 0
129

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 129 0 = 0 0
130

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 130 0 = 0 0
131

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 131 0 = 0 0
132

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 132 0 = 0 0
133

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 133 0 = 0 0
134

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 134 0 = 0 0
135

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 135 0 = 0 0
136

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 136 0 = 0 0
137

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 137 0 = 0 0
138

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 138 0 = 0 0
139

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 139 0 = 0 0
140

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 140 0 = 0 0
141

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 141 0 = 0 0
142

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 142 0 = 0 0
143

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 143 0 = 0 0
144

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 144 0 = 0 0
145

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 145 0 = 0 0
146

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 146 0 = 0 0
147

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 147 0 = 0 0
148

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 148 0 = 0 0
149

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 149 0 = 0 0
150

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 150 0 = 0 0
151

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 151 0 = 0 0
152

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 152 0 = 0 0
153

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 153 0 = 0 0
154

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 154 0 = 0 0
155

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 155 0 = 0 0
156

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 156 0 = 0 0
157

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 157 0 = 0 0
158

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 158 0 = 0 0
159

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 159 0 = 0 0
160

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 160 0 = 0 0
161

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 161 0 = 0 0
162

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 162 0 = 0 0
163

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 163 0 = 0 0
164

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 164 0 = 0 0
165

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 165 0 = 0 0
166

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 166 0 = 0 0
167

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 167 0 = 0 0
168

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 168 0 = 0 0
169

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 169 0 = 0 0
170

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 170 0 = 0 0
171

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 171 0 = 0 0
172

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 172 0 = 0 0
173

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 173 0 = 0 0
174

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 174 0 = 0 0
175

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 175 0 = 0 0
176

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 176 0 = 0 0
177

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 177 0 = 0 0
178

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 178 0 = 0 0
179

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 179 0 = 0 0
180

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 180 0 = 0 0
181

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 181 0 = 0 0
182

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 182 0 = 0 0
183

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 183 0 = 0 0
184

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 184 0 = 0 0
185

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 185 0 = 0 0
186

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 186 0 = 0 0
187

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 187 0 = 0 0
188

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 188 0 = 0 0
189

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 189 0 = 0 0
190

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 190 0 = 0 0
191

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 191 0 = 0 0
192

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 192 0 = 0 0
193

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 193 0 = 0 0
194

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 194 0 = 0 0
195

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 195 0 = 0 0
196

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 196 0 = 0 0
197

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 197 0 = 0 0
198

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 198 0 = 0 0
199

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 199 0 = 0 0
200

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 200 0 = 0 0
201

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 201 0 = 0 0
202

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 202 0 = 0 0
203

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 203 0 = 0 0
204

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 204 0 = 0 0
205

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 205 0 = 0 0
206

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 206 0 = 0 0
207

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 207 0 = 0 0
208

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 208 0 = 0 0
209

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 209 0 = 0 0
210

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 210 0 = 0 0
211

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 211 0 = 0 0
212

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 212 0 = 0 0
213

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 213 0 = 0 0
214

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 214 0 = 0 0
215

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 215 0 = 0 0
216

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 216 0 = 0 0
217

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 217 0 = 0 0
218

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 218 0 = 0 0
219

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 219 0 = 0 0
220

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 220 0 = 0 0
221

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 221 0 = 0 0
222

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 222 0 = 0 0
223

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 223 0 = 0 0
224

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 224 0 = 0 0
225

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 225 0 = 0 0
226

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 226 0 = 0 0
227

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 227 0 = 0 0
228

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 228 0 = 0 0
229

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 229 0 = 0 0
230

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 230 0 = 0 0
231

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 231 0 = 0 0
232

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 232 0 = 0 0
233

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 233 0 = 0 0
234

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 234 0 = 0 0
235

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 235 0 = 0 0
236

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 236 0 = 0 0
237

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 237 0 = 0 0
238

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 238 0 = 0 0
239

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 239 0 = 0 0
240

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 240 0 = 0 0
241

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 241 0 = 0 0
242

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 242 0 = 0 0
243

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 243 0 = 0 0
244

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 244 0 = 0 0
245

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 245 0 = 0 0
246

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 246 0 = 0 0
247

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 247 0 = 0 0
248

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 248 0 = 0 0
249

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 249 0 = 0 0
250

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 250 0 = 0 0
251

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 251 0 = 0 0
252

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 252 0 = 0 0
253

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 253 0 = 0 0
254

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 254 0 = 0 0
255

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 255 0 = 0 0
256

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 256 0 = 0 0
257

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 257 0 = 0 0
258

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 258 0 = 0 0
259

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 259 0 = 0 0
260

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 260 0 = 0 0
261

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 261 0 = 0 0
262

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 262 0 = 0 0
263

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 263 0 = 0 0
264

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 264 0 = 0 0
265

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 265 0 = 0 0
266

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 266 0 = 0 0
267

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 267 0 = 0 0
268

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 268 0 = 0 0
269

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 269 0 = 0 0
270

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 270 0 = 0 0
271

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 271 0 = 0 0
272

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 272 0 = 0 0
273

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 273 0 = 0 0
274

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 274 0 = 0 0
275

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 275 0 = 0 0
276

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 276 0 = 0 0
277

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 277 0 = 0 0
278

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 278 0 = 0 0
279

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 279 0 = 0 0
280

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 280 0 = 0 0
281

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 281 0 = 0 0
282

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 282 0 = 0 0
283

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 283 0 = 0 0
284

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 284 0 = 0 0
285

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 285 0 = 0 0
286

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 286 0 = 0 0
287

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 287 0 = 0 0
288

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 288 0 = 0 0
289

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 289 0 = 0 0
290

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 290 0 = 0 0
291

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 291 0 = 0 0
292

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 292 0 = 0 0
293

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 293 0 = 0 0
294

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 294 0 = 0 0
295

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 295 0 = 0 0
296

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 296 0 = 0 0
297

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 297 0 = 0 0
298

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 298 0 = 0 0
299

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 299 0 = 0 0
300

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 300 0 = 0 0
301

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 301 0 = 0 0
302

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 302 0 = 0 0
303

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 303 0 = 0 0
304

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 304 0 = 0 0
305

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 305 0 = 0 0
306

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 306 0 = 0 0
307

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 307 0 = 0 0
308

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 308 0 = 0 0
309

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 309 0 = 0 0
310

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 310 0 = 0 0
311

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 311 0 = 0 0
312

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 312 0 = 0 0
313

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 313 0 = 0 0
314

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 314 0 = 0 0
315

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 315 0 = 0 0
316

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 316 0 = 0 0
317

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 317 0 = 0 0
318

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 318 0 = 0 0
319

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 319 0 = 0 0
320

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 320 0 = 0 0
321

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 321 0 = 0 0
322

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 322 0 = 0 0
323

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 323 0 = 0 0
324

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 324 0 = 0 0
325

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 325 0 = 0 0
326

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 326 0 = 0 0
327

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 327 0 = 0 0
328

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 328 0 = 0 0
329

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 329 0 = 0 0
330

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 330 0 = 0 0
331

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 331 0 = 0 0
332

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 332 0 = 0 0
333

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 333 0 = 0 0
334

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 334 0 = 0 0
335

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 335 0 = 0 0
336

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 336 0 = 0 0
337

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 337 0 = 0 0
338

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 338 0 = 0 0
339

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 339 0 = 0 0
340

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 340 0 = 0 0
341

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 341 0 = 0 0
342

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 342 0 = 0 0
343

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 343 0 = 0 0
344

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 344 0 = 0 0
345

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 345 0 = 0 0
346

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 346 0 = 0 0
347

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 347 0 = 0 0
348

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 348 0 = 0 0
349

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 349 0 = 0 0
350

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 350 0 = 0 0
351

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 351 0 = 0 0
352

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 352 0 = 0 0
353

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 353 0 = 0 0
354

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 354 0 = 0 0
355

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 355 0 = 0 0
356

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 356 0 = 0 0
357

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 357 0 = 0 0
358

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 358 0 = 0 0
359

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 359 0 = 0 0
360

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 360 0 = 0 0
361

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 361 0 = 0 0
362

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 362 0 = 0 0
363

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 363 0 = 0 0
364

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 364 0 = 0 0
365

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 365 0 = 0 0
366

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 366 0 = 0 0
367

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 367 0 = 0 0
368

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 368 0 = 0 0
369

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 369 0 = 0 0
370

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 370 0 = 0 0
371

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 371 0 = 0 0
372

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 372 0 = 0 0
373

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 373 0 = 0 0
374

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 374 0 = 0 0
375

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 375 0 = 0 0
376

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 376 0 = 0 0
377

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 377 0 = 0 0
378

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 378 0 = 0 0
379

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 379 0 = 0 0
380

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 380 0 = 0 0
381

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 381 0 = 0 0
382

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 382 0 = 0 0
383

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 383 0 = 0 0
384

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 384 0 = 0 0
385

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 385 0 = 0 0
386

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 386 0 = 0 0
387

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 387 0 = 0 0
388

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 388 0 = 0 0
389

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 389 0 = 0 0
390

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 390 0 = 0 0
391

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 391 0 = 0 0
392

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 392 0 = 0 0
393

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 393 0 = 0 0
394

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 394 0 = 0 0
395

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 395 0 = 0 0
396

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 396 0 = 0 0
397

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 397 0 = 0 0
398

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 398 0 = 0 0
399

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 399 0 = 0 0
400

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 400 0 = 0 0
401

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 401 0 = 0 0
402

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 402 0 = 0 0
403

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 403 0 = 0 0
404

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 404 0 = 0 0
405

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 405 0 = 0 0
406

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 406 0 = 0 0
407

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 407 0 = 0 0
408

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 408 0 = 0 0
409

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 409 0 = 0 0
410

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 410 0 = 0 0
411

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 411 0 = 0 0
412

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 412 0 = 0 0
413

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 413 0 = 0 0
414

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 414 0 = 0 0
415

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 415 0 = 0 0
416

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 416 0 = 0 0
417

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 417 0 = 0 0
418

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 418 0 = 0 0
419

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 419 0 = 0 0
420

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 420 0 = 0 0
421

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 421 0 = 0 0
422

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 422 0 = 0 0
423

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 423 0 = 0 0
424

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 424 0 = 0 0
425

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 425 0 = 0 0
426

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 426 0 = 0 0
427

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 427 0 = 0 0
428

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 428 0 = 0 0
429

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 429 0 = 0 0
430

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 430 0 = 0 0
431

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 431 0 = 0 0
432

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 432 0 = 0 0
433

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 433 0 = 0 0
434

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 434 0 = 0 0
435

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 435 0 = 0 0
436

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 436 0 = 0 0
437

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 437 0 = 0 0
438

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 438 0 = 0 0
439

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 439 0 = 0 0
440

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 440 0 = 0 0
441

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 441 0 = 0 0
442

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 442 0 = 0 0
443

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 443 0 = 0 0
444

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 444 0 = 0 0
445

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 445 0 = 0 0
446

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 446 0 = 0 0
447

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 447 0 = 0 0
448

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 448 0 = 0 0
449

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 449 0 = 0 0
450

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 450 0 = 0 0
451

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 451 0 = 0 0
452

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 452 0 = 0 0
453

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 453 0 = 0 0
454

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 454 0 = 0 0
455

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 455 0 = 0 0
456

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 456 0 = 0 0
457

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 457 0 = 0 0
458

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 458 0 = 0 0
459

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 459 0 = 0 0
460

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 460 0 = 0 0
461

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 461 0 = 0 0
462

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 462 0 = 0 0
463

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 463 0 = 0 0
464

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 464 0 = 0 0
465

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 465 0 = 0 0
466

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 466 0 = 0 0
467

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 467 0 = 0 0
468

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 468 0 = 0 0
469

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 469 0 = 0 0
470

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 470 0 = 0 0
471

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 471 0 = 0 0
472

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 472 0 = 0 0
473

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 473 0 = 0 0
474

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 474 0 = 0 0
475

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 475 0 = 0 0
476

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 476 0 = 0 0
477

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 477 0 = 0 0
478

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 478 0 = 0 0
479

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 479 0 = 0 0
480

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 480 0 = 0 0
481

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 481 0 = 0 0
482

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 482 0 = 0 0
483

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 483 0 = 0 0
484

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 484 0 = 0 0
485

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 485 0 = 0 0
486

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 486 0 = 0 0
487

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 487 0 = 0 0
488

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 488 0 = 0 0
489

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 489 0 = 0 0
490

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 490 0 = 0 0
491

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 491 0 = 0 0
492

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 492 0 = 0 0
493

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 493 0 = 0 0
494

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 494 0 = 0 0
495

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 495 0 = 0 0
496

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 496 0 = 0 0
497

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 497 0 = 0 0
498

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 498 0 = 0 0
499

0 = ERROR:#DIV/0! = ERROR:#DIV/0! 499 0 = 0 0
500

0 = ERROR:#DIV/0! 0 ERROR:#DIV/0! 500 0 = 0 0
501

0 0 0 0

MIDPOINT SUMS FOR THE GRAPH OF A FUNCTION

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x
f(x)

1. Set Excel for Automatic Calculation.
2. Enter a formula, in terms of the letter x, for = f(x) in Cell C18. Constants s, t, u, v, or w may be used; if values are entered in Cells L23:L27. (The value of f(0) will appear in Cell C18.)
3. Click on the Sum button located in Cell I21. This runs the macro, Sum.
4. Cell F18 will display the value of f(x) for any number x that is entered in Cell E18.
5. Enter values for a and b, to see the graph of f(x) over the interval [a, b]. Constants s, t, u, v, or w may be used; if values are entered in Cells K25:K29. If these constant names are used, they must be entered in Cells H18:I18 preceded with “=” signs. For example, =s.
6. Move the Number of subintervals slider to set a value for n in Cell C22. Clicking on an arrow at the end of the scroll bar increases or decreases n by 1. Clicking in the scroll bar increases or decreased n by 10. The width, Dx, of each subinterval and the midpoint sum will be calculated and displayed.

Mathematics for Business Decisions, Part 2
Release 2, 2009
Published and Distributed by
The Mathematical Association of America
© 2009 by The Arizona Board of Regents for
The University of Arizona. All rights reserved.

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