David (bigd4316)

Race #38597

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Official speed 102.54 wpm (101.11 seconds elapsed during race)
Without ending ping 102.92 wpm (377 ms delay sending score to TypeRacer’s server)
Timerless 103.52 wpm (578 ms elapsed before first character typed; 100.16 seconds elapsed during race)
Timerless minus one 103.40 wpm, ignoring the first character typed
Race Start March 12, 2024 6:06:37pm UTC
Race Finish March 12, 2024 6:08:18pm UTC
Outcome Win (1 of 3)
Accuracy 98.1%
Points 276.86
Text #4940058 (Length: 864 characters)

Calculus is a tool that helps us understand how a change in one quantity is related to a change in another. How does the speed of a falling object change as a function of time? How does the level of water in a barrel change as a function of the amount of liquid poured into it? We see change occurring in nearly everything we observe in the world and universe, and powerful modern instruments help us see more and more. In this section we introduce the ideas of average and instantaneous rates of change, and show that they are closely related to the slope of a curve at a point P on the curve. We give precise developments of these important concepts in the next chapter, but for now we use an informal approach so you will see how they lead naturally to the main idea of this chapter, the limit. The idea of a limit plays a foundational role throughout calculus.
Characters typed Calcululss is a tool that helps us understand how a change in one quantity tiis relateed to a change inan another. How does the speed of a falling object change as a funtion ction of time? How does the level of water in a barrel change as a function of the amount of liquid poured into it? We see change occurring in nearly everythinhg we g we bobserve in the world and universe, and powerful modneern instruments help us see more and oremore. In this section we introduce the ideas of average and instantaneous rates of hachanges, , and show that they are closely related to the slop ee of a curve at a point P on the curve. We give precise developments of these important comnvceps ts in the next chapter, but for now we use an informal approach so you will see how they lead neaturally to the main idea of this chapter, the limit. The idea of a limit plays a foundational role thoghroughtouout calculus.
Timing
Character C a l c u l u l s -s -l s i s a t o o l t h
Milliseconds 578 159 82 125 133 156 160 190 193 269 106 69 108 163 56 86 63 70 136 76 122 158 54 73 82
Character a t h e l p s u s u n d e r s t a n d h o
Milliseconds 45 58 30 162 239 129 63 123 61 135 242 131 168 157 23 162 75 152 140 58 87 77 72 101 60
Character w a c h a n g e i n o n e q u a n t i t
Milliseconds 56 68 77 69 91 91 83 73 85 48 62 13 86 64 154 32 103 81 221 78 117 59 158 23 136
Character y t i -i -t i s r e l a t e -e e d t o a c
Milliseconds 88 74 17 151 330 115 281 67 77 148 51 137 81 105 37 188 741 144 70 111 34 44 97 86 116
Character h a n g e i n a n -n -a a n o t h e r . H o w
Milliseconds 83 98 58 86 25 64 39 82 118 167 322 115 78 129 101 128 88 76 86 48 33 51 183 134 54
Character d o e s t h e s p e e d o f a f a l l
Milliseconds 115 70 92 86 41 75 81 42 47 82 139 81 97 117 137 77 141 84 109 63 55 132 58 55 123
Character i n g o b j e c t c h a n g e a s a f u
Milliseconds 55 78 114 56 113 290 160 98 174 109 82 122 83 69 58 121 41 101 41 75 99 73 85 104 94
Character n t i o n - -n -o -i -t c t i o n o f t i m e ?
Milliseconds 189 248 61 66 46 67 275 124 141 160 105 109 317 48 62 77 64 163 65 70 113 54 147 79 182
Character H o w d o e s t h e l e v e l o f w a
Milliseconds 65 211 220 100 133 94 85 93 33 87 58 66 23 86 106 52 136 62 108 42 198 88 108 109 39
Character t e r i n a b a r r e l c h a n g e a s
Milliseconds 145 157 54 84 44 85 89 127 84 175 135 151 122 77 150 154 200 116 100 60 97 39 115 66 68
Character a f u n c t i o n o f t h e a m o u n t
Milliseconds 98 86 73 100 78 148 38 154 65 61 56 49 182 93 68 97 37 22 90 207 97 138 49 163 115
Character o f l i q u i d p o u r e d i n t o i t
Milliseconds 68 156 92 63 174 42 240 102 32 121 128 158 169 138 161 114 148 89 64 77 143 56 42 174 77
Character ? W e s e e c h a n g e o c c u r r i n g
Milliseconds 208 46 213 173 67 108 57 127 101 125 95 94 67 98 45 96 218 77 151 81 125 136 98 43 108
Character i n n e a r l y e v e r y t h i n h g w e
Milliseconds 76 77 63 77 123 83 48 63 229 82 96 255 157 113 71 42 116 85 50 128 7 61 90 110 61
Character - -e -w - -g -h g w e b -b o b s e r v e i n
Milliseconds 129 249 125 140 144 144 126 106 113 177 41 125 243 227 165 74 261 80 82 134 152 116 41 82 58
Character t h e w o r l d a n d u n i v e r s e , a
Milliseconds 91 36 67 77 97 64 84 77 98 77 77 45 112 15 116 169 49 89 123 74 84 66 84 54 104
Character n d p o w e r f u l m o d n e -e -n e r n i n
Milliseconds 45 87 57 99 167 70 54 45 152 56 99 81 177 53 176 102 70 175 97 87 49 63 88 143 50
Character s t r u m e n t s h e l p u s s e e m o r
Milliseconds 108 169 170 72 145 64 88 96 65 54 117 118 42 64 43 182 85 87 86 24 164 163 199 68 68
Character e a n d o r e -e -r -o m o r e . I n t h i s
Milliseconds 39 88 98 90 60 68 132 87 44 308 119 121 200 35 69 33 113 36 217 134 73 152 51 42 64
Character s e c t i o n w e i n t r o d u c e t h e
Milliseconds 93 75 107 201 134 47 69 31 51 115 58 84 176 59 186 179 83 180 106 102 178 112 105 47 81
Character i d e a s o f a v e r a g e a n d i n s
Milliseconds 47 219 66 129 56 125 106 151 73 76 69 151 141 89 64 172 54 92 104 72 85 51 124 60 106
Character t a n t a n e o u s r a t e s o f h a -a -h c
Milliseconds 111 115 119 195 112 601 313 77 48 99 87 124 55 145 57 77 90 155 73 76 170 3 215 107 84
Character h a n g e s , - -, -s , a n d s h o w t h a
Milliseconds 92 82 75 80 48 71 52 53 351 114 135 240 32 62 88 52 84 129 102 25 142 126 160 98 72
Character t t h e y a r e c l o s e l y r e l a t e
Milliseconds 67 50 113 48 82 59 33 74 63 43 59 155 80 119 24 81 137 53 63 133 39 111 92 91 56
Character d t o t h e s l o p e -e - e o f a c
Milliseconds 147 102 71 56 56 103 67 77 88 102 102 142 57 74 84 267 105 77 90 164 79 71 88 76 113
Character u r v e a t a p o i n t P o n t h e
Milliseconds 103 97 171 96 118 82 53 90 67 75 128 121 70 48 72 111 133 97 143 83 76 83 78 30 64
Character c u r v e . W e g i v e p r e c i s e d e
Milliseconds 141 94 76 153 70 102 30 216 142 95 137 81 95 99 73 44 120 70 178 139 212 47 126 234 170
Character v e l o p m e n t s o f t h e s e i m p o r
Milliseconds 170 113 112 168 50 212 102 92 99 51 65 149 109 70 122 80 82 133 35 90 58 210 81 198 121
Character t a n t c o m -m n v -v c e p s - -s t s i n
Milliseconds 167 91 64 115 86 144 75 88 444 137 92 287 86 166 89 115 128 249 127 137 43 53 72 72 73
Character t h e n e x t c h a p t e r , b u t f o r
Milliseconds 92 41 59 69 119 62 184 62 94 149 109 84 111 203 163 41 85 21 118 71 102 53 131 69 81
Character n o w w e u s e a n i n f o r m a l a
Milliseconds 61 121 53 88 78 114 66 78 142 100 56 173 149 107 97 120 61 124 97 83 95 94 95 42 168
Character p p r o a c h s o y o u w i l l s e e h
Milliseconds 112 119 157 67 102 138 99 211 176 106 133 172 89 48 52 80 94 137 131 33 65 59 176 167 400
Character o w t h e y l e a d n e -e a t u r a l l y
Milliseconds 46 144 100 119 74 63 81 36 160 52 46 152 75 150 85 274 93 165 119 81 52 80 127 65 61
Character t o t h e m a i n i d e a o f t h i s
Milliseconds 173 49 50 86 59 58 17 147 85 87 61 77 164 124 143 17 153 151 92 73 93 53 44 59 83
Character c h a p t e r , t h e l i m i t . T h e i
Milliseconds 124 67 78 81 159 133 51 76 32 133 75 133 99 138 40 197 169 113 93 43 208 73 78 42 139
Character d e a o f a l i m i t p l a y s a f o
Milliseconds 81 151 28 106 157 54 88 53 80 244 40 181 206 141 143 180 165 79 81 94 97 90 85 101 72
Character u n d a t i o n a l r o l e t h o g h -h -g -o r
Milliseconds 53 115 86 75 129 74 28 77 133 95 22 157 66 136 93 104 109 61 107 150 80 254 106 469 173
Character o u g h t o u -u -o -t o u t c a l c u l u s .
Milliseconds 129 40 116 92 75 92 44 316 113 147 262 53 115 95 212 127 131 271 81 142 239 158 70
WPM Timing
Seconds WPM
2.02 41.54
4.04 77.14
6.07 87.03
8.09 100.88
10.11 96.13
12.13 93.96
14.16 93.25
16.18 98.65
18.2 100.22
20.22 96.13
22.24 96.02
24.27 98.41
26.29 99.05
28.31 101.73
30.33 102.46
32.36 102.36
34.38 102.97
36.4 103.52
38.42 100.25
40.44 98.8
42.47 101.44
44.49 101.69
46.51 102.68
48.53 102.36
50.56 102.3
52.58 102.7
54.6 103.3
56.62 102.36
58.64 102.11
60.67 101.47
62.69 102.98
64.71 102.92
66.73 103.58
68.76 104.19
70.78 103.93
72.8 104.34
74.82 103.44
76.84 102.75
78.87 103.16
80.89 103.55
82.91 103.63
84.93 103.56
86.96 103.5
88.98 104.25
91 104.7
93.02 105.01
95.05 105.04
97.07 104.59
99.09 103.18
101.11 102.54