BarbBlackburn (3xx8iycrr3xyxs2)

Race #13280

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Official speed 91.72 wpm (113.04 seconds elapsed during race)
Without ending ping 91.95 wpm (284 ms delay sending score to TypeRacer’s server)
Timerless 92.30 wpm (427 ms elapsed before first character typed; 112.33 seconds elapsed during race)
Timerless minus one 92.19 wpm, ignoring the first character typed
Race Start October 5, 2023 4:36:04am UTC
Race Finish October 5, 2023 4:37:57am UTC
Outcome Win (1 of 4)
Opponents 2. dylan_1231 (63.25 wpm)
Accuracy 98.3%
Points 247.63
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 Calculus is a tool that heplps us understand how a change in one quantity is realtelated to a chnageange 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 everhtything we observe in the world and universe, and powerful modern instruments help us see more and more. In this section we introucduce the ideas of average and instantaneous rates of change, and show that they are closely reallated to ehthe slope of a curve at a point P on the curve. We give precise developments o fthf ff these important concepts in the next chanppter, but for now we use an informal approach so you will see how they hlead naturally to the main idea o ff this chapter, the limit. The idea of a limit plays a foundational role through out calucculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 427 168 95 417 150 185 259 133 97 112 149 88 110 94 182 53 137 174 100 142 84 73 68 39 135
Character e p -p l p s u s u n d e r s t a n d h o w
Milliseconds 160 424 456 197 140 144 105 129 95 88 183 196 116 159 55 143 105 146 15 160 62 129 50 75 77
Character a c h a n g e i n o n e q u a n t i t y
Milliseconds 104 109 173 94 75 53 145 61 96 101 84 99 138 79 105 106 180 77 163 106 217 102 555 95 80
Character i s r e a l t e -e -t -l -a l a t e d t o a c
Milliseconds 137 103 101 161 64 112 48 178 90 259 154 162 123 182 91 129 81 79 144 142 47 118 214 78 213
Character h n a g e -e -g -a -n a n g e i n a n o t h e r .
Milliseconds 84 134 65 143 77 222 146 151 131 98 83 128 49 119 119 76 76 128 85 77 64 61 122 73 60
Character H o w d o e s t h e s p e e d o f a
Milliseconds 80 210 112 136 113 120 90 106 132 62 119 25 71 75 129 87 130 154 153 89 129 47 189 132 88
Character f a l l i n g o b j e c t c h a n g e a s
Milliseconds 174 161 235 221 123 72 136 76 117 118 137 213 176 122 86 102 62 63 86 53 79 134 61 96 72
Character a f u n c t i o n o f t i m e ? H o w d
Milliseconds 130 27 127 129 27 112 143 53 39 77 108 136 31 225 117 54 56 27 294 137 176 176 216 133 143
Character o e s t h e l e v e l o f w a t e r i n
Milliseconds 83 107 111 89 100 22 78 83 144 141 123 93 44 130 180 127 86 169 189 47 97 60 92 85 62
Character a b a r r e l c h a n g e a s a f u n
Milliseconds 151 41 123 128 286 99 160 228 111 203 98 103 49 83 61 72 120 88 169 96 135 79 76 178 48
Character c t i o n o f t h e a m o u n t o f l i
Milliseconds 131 164 52 22 73 93 170 111 80 100 36 62 114 131 92 135 64 141 118 94 99 116 93 169 62
Character q u i d p o u r e d i n t o i t ? W e s
Milliseconds 224 84 85 474 121 215 17 155 215 253 157 83 64 76 111 79 105 143 113 294 513 227 213 84 146
Character e e c h a n g e o c c u r r i n g i n n e
Milliseconds 73 155 171 163 112 19 149 78 67 97 138 148 162 122 110 199 141 72 97 95 110 70 119 114 61
Character a r l y e v e r h t -t -h y t h i n g w e o b
Milliseconds 158 48 61 117 69 122 100 106 82 92 90 338 140 130 173 73 56 116 28 172 51 110 71 141 155
Character s e r v e i n t h e w o r l d a n d u n
Milliseconds 159 69 60 173 100 159 56 116 108 81 90 0 161 69 116 118 23 207 77 90 44 124 37 134 72
Character i v e r s e , a n d p o w e r f u l m o d e
Milliseconds 159 132 152 74 124 121 74 70 117 44 98 74 101 44 120 100 84 167 95 133 105 173 136 173 186
Character r n i n s t r u m e n t s h e l p u s s e
Milliseconds 92 119 131 150 67 167 104 131 48 166 108 49 103 116 108 139 181 120 131 105 143 91 121 112 138
Character e m o r e a n d m o r e . I n t h i s
Milliseconds 168 60 115 52 72 46 75 104 22 100 88 106 52 99 15 112 82 183 182 105 135 51 61 163 153
Character s e c t i o n w e i n t r o u c -c -u d u c e
Milliseconds 336 10 137 200 67 38 54 110 99 93 88 217 105 200 162 208 200 172 281 132 104 93 99 165 77
Character t h e i d e a s o f a v e r a g e a n d
Milliseconds 97 43 66 104 85 107 156 207 470 111 146 130 92 191 312 95 120 125 216 84 128 93 56 84 83
Character i n s t a n t a n e o u s r a t e s o f c h
Milliseconds 126 63 151 181 126 327 228 217 171 195 312 112 181 105 198 139 89 63 146 106 157 131 81 140 58
Character a n g e , a n d s h o w t h a t t h e y
Milliseconds 51 104 68 79 92 85 48 91 81 45 167 414 26 235 174 71 75 85 57 53 125 20 96 82 61
Character a r e c l o s e l y r e a l -l -a l a t e d t
Milliseconds 115 64 67 49 219 27 196 55 66 99 182 101 261 96 157 13 463 145 154 69 96 71 138 57 144
Character o e h -h -e t h e s l o p e o f a c u r v
Milliseconds 46 169 183 40 507 131 77 55 89 83 155 55 337 120 184 111 166 131 88 112 83 143 132 120 202
Character e a t a p o i n t P o n t h e c u r
Milliseconds 88 66 124 256 72 101 77 255 49 46 132 103 111 204 179 160 81 140 140 40 62 77 152 81 114
Character v e . W e g i v e p r e c i s e d e v e l
Milliseconds 177 89 115 56 284 190 140 160 81 116 46 92 233 86 72 244 176 132 71 110 160 217 118 86 75
Character o p m e n t s o f t h -h -t -f f - -f - f -f -
Milliseconds 182 135 133 115 88 69 140 75 99 130 0 187 76 298 145 152 162 111 190 151 128 149 0 472 143
Character f t h e s e i m p o r t a n t c o n c e p t
Milliseconds 76 108 147 64 93 168 72 92 115 73 118 0 149 55 141 103 86 91 112 35 30 112 202 128 126
Character s i n t h e n e x t c h a n p -p -n p t e r
Milliseconds 123 42 86 88 83 79 79 32 83 150 121 163 103 53 149 42 71 83 167 278 150 161 98 106 91
Character , b u t f o r n o w w e u s e a n i
Milliseconds 64 94 129 66 108 68 107 35 130 18 148 27 190 266 234 93 112 139 74 73 85 192 104 112 125
Character n f o r m a l a p p r o a c h s o y o u w
Milliseconds 76 85 144 117 223 186 97 104 163 100 136 145 81 118 128 80 133 156 67 119 129 92 55 72 95
Character i l l s e e h o w t h e y h -h l e a d n
Milliseconds 84 196 144 78 106 79 176 95 125 43 97 73 107 99 32 132 100 153 306 196 95 117 62 86 92
Character a t u r a l l y t o t h e m a i n i d e a
Milliseconds 103 103 64 102 160 102 108 129 63 150 40 162 135 63 75 87 151 141 68 65 91 143 105 163 76
Character o f -f - f t h i s c h a p t e r , t h e
Milliseconds 102 116 138 30 394 146 129 95 155 41 214 164 102 127 156 0 344 273 179 90 86 87 138 27 101
Character l i m i t . T h e i d e a o f a l i m
Milliseconds 45 278 77 84 169 172 100 115 209 88 52 88 67 144 191 106 64 57 145 78 135 104 174 15 154
Character i t p l a y s a f o u n d a t i o n a l r
Milliseconds 157 157 88 85 88 79 91 141 103 100 88 340 68 57 174 48 177 104 56 8 72 199 135 244 242
Character o l e t h r o u g h - o u t c a l u c -c -u c
Milliseconds 69 142 88 93 91 73 101 73 41 66 88 94 393 188 43 97 118 215 251 162 171 121 301 131 94
Character u l u s .
Milliseconds 87 133 121 162 100
WPM Timing
Seconds WPM
2.26 58.39
4.52 69
6.78 74.31
9.04 84.93
11.3 82.8
13.56 78.73
15.83 76.58
18.09 82.27
20.35 82.57
22.61 86.52
24.87 87.34
27.13 89.35
29.39 90.64
31.65 92.89
33.91 92.36
36.17 91.89
38.43 91.48
40.69 92.3
42.96 91.63
45.22 93.15
47.48 94.53
49.74 94.58
52 95.54
54.26 95.76
56.52 94.48
58.78 94.32
61.04 94.17
63.3 93.08
65.56 93.71
67.82 94.66
70.08 93.66
72.35 92.56
74.61 92.81
76.87 92.89
79.13 92.81
81.39 92.15
83.65 90.38
85.91 91.35
88.17 91.19
90.43 91.69
92.69 91.79
94.95 92.13
97.21 92.33
99.47 92.77
101.74 92.12
104 92.08
106.26 92.49
108.52 92.67
110.78 92.62
113.04 91.72