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Race #55

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Official speed 80.47 wpm (128.84 seconds elapsed during race)
Without ending ping 80.65 wpm (288 ms delay sending score to TypeRacer’s server)
Timerless 81.13 wpm (757 ms elapsed before first character typed; 127.80 seconds elapsed during race)
Timerless minus one 81.03 wpm, ignoring the first character typed
Race Start December 6, 2023 8:47:25am UTC
Race Finish December 6, 2023 8:49:33am UTC
Outcome No win (3 of 4)
Opponents 4. ryanwalterg (80.06 wpm)
Accuracy 97.6%
Points 217.27
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 helps us understand how a change in one quantity is related to a change in another. How dowses the speed of a falling object change as a function of time? How does the lvevel of water in a barerel chagne ange as a function of the amount of liquid poured into it? We see chagnge occurring in nearly everything we observe in the world and universe, and powerful modern instruments hel p us see more and more. In the sis section we introduce the dideas of average and instantaneous rates of change, and show that they are closely related to the slope oaf a curve at a point P on the curve. We iggive precise developments owf these important concepts in the next chapter, but for now ewe use an informal apporaroach so yo wiu will see how they lead naturally to the main idea of the is chapter, the limit. The idea of a limit plays ar foundational role throught out calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 757 451 103 283 109 158 181 90 73 187 91 128 309 160 147 228 144 167 123 115 107 87 115 50 192
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 140 119 214 146 43 271 117 113 127 179 94 162 113 171 164 146 123 74 94 114 65 109 163 192 169
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 271 103 91 142 44 125 92 101 136 127 126 115 108 99 210 99 136 106 147 170 385 117 105 169 109
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 118 136 120 102 118 95 122 148 112 116 110 94 118 238 192 125 83 122 67 102 117 88 122 118 192
Character n o t h e r . H o w d o w s -s -w e s t h e
Milliseconds 122 87 94 99 92 78 96 220 211 92 108 287 158 127 89 202 309 186 107 122 104 100 80 78 44
Character s p e e d o f a f a l l i n g o b j e c t
Milliseconds 125 134 75 134 162 89 112 110 108 90 141 298 80 95 144 149 95 75 58 104 134 73 118 192 219
Character c h a n g e a s a f u n c t i o n o f
Milliseconds 135 289 20 93 99 46 132 90 134 148 130 92 129 95 115 158 134 245 127 68 101 147 83 118 118
Character t i m e ? H o w d o e s t h e l v -v e v e
Milliseconds 214 83 151 102 231 175 216 103 102 96 126 97 95 144 133 100 92 63 104 234 134 470 82 84 66
Character l o f w a t e r i n a b a r e -e r e l
Milliseconds 97 173 98 127 50 319 146 89 127 64 41 96 119 150 104 149 138 346 153 155 415 36 93 108 299
Character c h a g n e a -a - -e -n -g n g e a s a f u n
Milliseconds 143 112 41 131 15 107 90 104 284 163 155 169 109 182 71 113 117 170 178 141 256 519 152 99 164
Character c t i o n o f t h e a m o u n t o f l i
Milliseconds 75 233 51 106 465 162 91 92 81 127 79 82 47 265 228 128 108 163 78 60 90 88 80 145 161
Character q u i d p o u r e d i n t o i t ? W e s
Milliseconds 113 115 130 108 83 307 163 121 50 110 162 126 144 107 124 79 126 236 111 275 155 251 78 137 242
Character e e c h a g -g n g e o c c u r r i n g i n
Milliseconds 177 126 110 168 94 17 229 483 200 46 118 145 214 274 276 165 98 146 121 101 46 110 197 128 161
Character n e a r l y e v e r y t h i n g w e o b s e
Milliseconds 316 68 76 92 67 159 76 133 142 96 127 53 244 74 127 94 32 98 54 138 116 206 149 379 147
Character r v e i n t h e w o r l d a n d u n i v
Milliseconds 220 192 137 110 95 107 122 77 94 67 18 121 79 83 146 121 82 163 92 96 78 374 166 91 64
Character e r s e , a n d p o w e r f u l m o d e r n
Milliseconds 131 100 154 160 99 181 100 227 132 125 141 129 101 85 48 196 109 157 148 373 136 98 145 120 106
Character i n s t r u m e n t s h e l - p u s s e
Milliseconds 124 185 132 95 196 160 107 174 65 114 128 175 125 179 139 136 326 512 225 138 116 108 376 94 155
Character e m o r e a n d m o r e . I n t h e s
Milliseconds 126 84 146 108 50 106 42 99 111 54 89 122 127 79 82 74 245 164 313 132 116 52 101 47 179
Character -s - -e i s s e c t i o n w e i n t r o d u c
Milliseconds 373 150 127 183 79 50 111 150 186 176 52 70 99 121 137 80 146 177 232 120 125 80 114 75 309
Character e t h e d -d i d e a s o f a v e r a g e
Milliseconds 204 111 121 61 84 77 178 282 208 88 164 81 134 113 103 116 54 635 98 141 337 152 129 134 87
Character a n d i n s t a n t a n e o u s r a t e s o
Milliseconds 93 73 73 63 131 128 84 145 111 126 60 607 93 119 499 98 77 107 226 119 126 135 134 61 127
Character f c h a n g e , a n d s h o w t h a t t
Milliseconds 107 77 276 130 102 116 45 129 109 172 108 58 103 57 99 102 78 82 101 88 108 27 103 55 100
Character h e y a r e c l o s e l y r e l a t e d t
Milliseconds 109 66 98 70 129 68 77 83 225 114 142 64 111 67 195 88 200 100 109 118 116 152 127 70 138
Character o t h e s l o p e o a -a f a c u r v e
Milliseconds 42 124 312 140 93 81 141 81 156 175 133 124 112 127 323 97 110 627 126 198 213 107 189 113 149
Character a t a p o i n t P o n t h e c u r v e
Milliseconds 109 105 78 92 115 181 189 119 161 97 85 295 166 125 147 138 108 80 74 40 195 27 173 391 113
Character . W e i g -g -i g i v e p r e c i s e d e v
Milliseconds 116 230 580 159 112 225 212 215 121 107 113 70 88 99 110 64 124 318 112 112 108 108 178 162 118
Character e l o p m e n t s o w -w f t h e s e i m p o
Milliseconds 74 100 162 134 175 107 73 575 288 145 92 185 419 73 135 79 98 85 193 130 106 127 145 147 120
Character r t a n t c o n c e p t s i n t h e n e x
Milliseconds 81 140 128 95 40 125 251 56 133 178 179 97 851 159 169 75 99 98 62 108 37 49 137 41 184
Character t c h a p t e r , b u t f o r n o w e -e
Milliseconds 205 124 159 74 102 108 71 109 78 90 162 114 96 100 93 165 79 97 49 135 68 115 78 214 334
Character w e u s e a n i n f o r m a l a p p o r a
Milliseconds 37 63 120 128 64 120 55 96 95 139 281 116 82 110 86 65 97 302 189 106 176 559 180 109 141
Character -a -r -o r o a c h s o y o w i -i -w - u w i l
Milliseconds 335 126 189 153 94 64 190 85 91 192 93 117 189 119 124 115 81 370 136 133 190 113 310 114 451
Character l s e e h o w t h e y l e a d n a t u r
Milliseconds 148 139 116 151 127 113 113 91 111 83 234 84 82 75 56 159 103 74 105 94 469 64 90 116 47
Character a l l y t o t h e m a i n i d e a o f
Milliseconds 107 67 136 210 110 125 93 147 100 81 72 41 167 103 88 97 116 207 93 161 62 119 118 133 170
Character t h e - -e i s c h a p t e r , t h e l i m
Milliseconds 132 82 79 236 315 117 180 53 76 151 90 89 100 63 108 80 157 192 52 116 22 95 138 139 159
Character i t . T h e i d e a o f a l i m i t p
Milliseconds 137 115 81 193 254 125 79 84 301 120 175 62 186 336 104 67 63 111 292 192 161 115 33 109 165
Character l a y s a r -r f o u n d a t i o n a l r o l
Milliseconds 185 98 99 86 93 63 152 376 164 108 66 98 156 84 84 369 96 34 107 94 107 358 267 88 157
Character e t h r o u g h t - -t o u t c a l c u l u s
Milliseconds 98 226 135 68 96 35 86 40 145 100 143 399 127 191 96 72 179 93 130 54 156 128 138 265 214
Character .
Milliseconds 112
WPM Timing
Seconds WPM
2.58 51.23
5.15 65.2
7.73 74.51
10.31 79.17
12.88 81.03
15.46 83.82
18.04 81.83
20.61 83.82
23.19 84.86
25.77 85.69
28.35 84.67
30.92 83.82
33.5 80.6
36.08 79.17
38.65 80.72
41.23 80.91
43.81 79.99
46.38 79.94
48.96 80.64
51.54 81.73
54.11 82.05
56.69 81.92
59.27 80.99
61.84 81.69
64.42 80.84
67 81.14
69.58 80.2
72.15 80.5
74.73 80.77
77.31 82.27
79.88 82.77
82.46 81.93
85.04 81.99
87.61 81.63
90.19 81.29
92.77 80.85
95.34 80.93
97.92 81
100.5 81.67
103.07 81.73
105.65 80.64
108.23 79.94
110.8 80.14
113.38 80.54
115.96 80.41
118.54 80.79
121.11 80.75
123.69 80.72
126.27 80.88
128.84 80.47