Jason (jason_kenney)

Race #1409

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Official speed 73.66 wpm (140.75 seconds elapsed during race)
Without ending ping 73.75 wpm (172 ms delay sending score to TypeRacer’s server)
Timerless 74.00 wpm (474 ms elapsed before first character typed; 140.11 seconds elapsed during race)
Timerless minus one 73.91 wpm, ignoring the first character typed
Race Start October 11, 2023 3:34:00pm UTC
Race Finish October 11, 2023 3:36:21pm UTC
Outcome Win (1 of 5)
Accuracy 97.1%
Points 198.88
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 reallated to caa change in another. How does the speed of a falling ojebeheobject chnchange as a uncfunction of time? How does the level of water ina a barrel change as a funcation function of the amount of liquid pourd puopourdepupoured into it/? We csee change occurring in nearly everything we observe in the world and univsuniverse, and powefurful modern instrucments help us seemor see more and more. In this section we introcutintroduce the ideas of average and instantaneous rates of change,a and hosshow that they are closely related to the slope of a curve at a pointP P on the curve. We gie pgive precise developments of these importnimportant coneconcepts in the next chapter, ubut for now we use an informal approach, so so you will see how they lead naturally to the main idea of this chapte, r, the limit. The idea of a millimit plays a foundational role throughout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 474 371 119 98 493 144 164 125 53 87 105 82 128 127 139 88 164 163 99 88 115 21 80 86 89
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 108 104 112 150 80 373 125 80 94 199 57 168 80 182 87 106 50 142 85 151 186 83 60 87 112
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 179 97 85 98 85 65 77 52 78 117 211 66 70 90 258 73 167 83 363 120 133 204 399 146 103
Character r e a l -l -a l a t e d t o c a -a -c a c h a
Milliseconds 71 100 76 40 117 351 157 207 23 56 53 182 23 114 100 76 188 110 522 167 58 84 111 114 50
Character n g e i n a n o t h e r . H o w d o e s
Milliseconds 123 90 48 91 39 66 149 61 267 79 111 78 68 65 102 155 172 167 101 42 149 88 90 112 38
Character t h e s p e e d o f a f a l l i n g o j
Milliseconds 97 97 69 93 244 175 113 159 144 50 84 53 111 74 125 274 92 88 210 50 79 49 78 324 124
Character e -e -j b e -e h e -e -h -b -o o b j e c t c h n -c -h -n
Milliseconds 173 337 148 498 212 358 113 96 390 159 170 186 199 123 89 108 202 67 80 201 67 187 726 0 0
Character c h a n g e a s a u n c -c -n -u f u n c t i o
Milliseconds 275 91 89 86 82 60 86 89 127 43 117 68 476 185 62 442 168 174 86 122 176 56 150 30 81
Character n o f t i m e ? H o w d o e s t h e l
Milliseconds 58 64 109 63 64 140 64 69 41 271 125 214 237 77 71 108 96 73 105 30 84 60 85 71 67
Character e v e l o f w a t e r i n a - -a a b a
Milliseconds 116 60 110 77 85 133 59 113 96 77 170 110 102 79 48 82 75 99 418 161 75 67 126 162 231
Character r r e l c h a n g e a s a f u n c a t i o
Milliseconds 170 166 102 56 222 84 417 277 116 83 64 60 193 144 34 99 97 82 121 202 177 196 77 31 65
Character n -f -u -n -c -a -t -i -o -n - f u n c t i o n o f t
Milliseconds 72 53 557 0 0 0 0 0 0 0 0 0 500 116 186 71 112 46 84 42 89 91 58 81 94
Character h e a m o u n t o f l i q u i d p o u r d
Milliseconds 78 71 61 115 62 118 116 162 49 82 81 80 64 140 398 95 746 66 254 89 336 75 426 180 97
Character - -d -r -u -o -p p u -u o -o -p p o u r d e -e -p -o -u -r -d
Milliseconds 118 573 160 249 161 183 193 248 102 446 214 329 127 515 207 417 180 118 220 236 362 0 0 0 0
Character p u -u -p p o u r e d i n t o i t / -/ ? W e
Milliseconds 309 132 505 371 272 257 247 389 206 188 61 103 81 62 88 101 91 82 272 378 522 267 690 272 90
Character c -c s e e c h a n g e o c c u r r i n g i n
Milliseconds 154 325 59 39 184 127 64 131 158 22 300 43 106 272 118 179 136 52 331 108 61 61 98 87 59
Character n e a r l y e v e r y t h i n g w e o b s
Milliseconds 102 148 58 71 42 66 146 104 39 141 104 76 108 201 78 126 81 65 84 119 80 88 185 107 244
Character e r v e i n t h e w o r l d a n d u n i
Milliseconds 26 73 212 91 73 39 64 83 71 84 70 94 71 81 86 132 72 77 72 105 56 61 104 186 74
Character v s -u -n -i -v -s u n i v e r s e , a n d p o w e
Milliseconds 80 196 1030 0 0 0 0 385 214 93 152 161 95 100 31 118 81 37 102 52 72 82 29 67 46
Character f u -u -f r f u l m o d e r n i n s t r u c -c m
Milliseconds 407 128 309 130 55 155 38 151 120 74 90 119 232 78 75 126 31 82 56 78 105 111 151 304 99
Character e n t s h e l p u s s e e m o r -s -e -e -m -o
Milliseconds 86 105 82 87 102 377 216 89 50 176 21 158 103 165 77 136 107 110 82 98 446 0 0 0 0
Character -r - s e e m o r e a n d m o r e . I n t
Milliseconds 0 0 620 84 133 100 66 66 30 59 61 59 88 59 63 74 59 44 53 146 67 209 206 88 101
Character h i s s e c t i o n w e i n t r o c u -i -n -t
Milliseconds 35 71 89 64 101 69 178 92 40 75 58 70 332 80 69 106 73 191 81 81 173 253 636 0 0
Character -r -o -c -u t -t i n t r o d u c e t h e i d e a s
Milliseconds 0 0 0 0 326 382 163 447 109 64 114 465 116 84 176 75 86 42 94 52 75 57 165 63 171
Character o f a v e r a g e a n d i n s t a n t a n
Milliseconds 62 124 70 86 146 115 140 79 148 71 73 74 50 110 44 84 127 80 206 110 159 122 283 222 212
Character e o u s r a t e s o f c h a n g e , a -a a
Milliseconds 389 348 88 150 101 407 103 93 54 136 0 311 61 81 162 103 86 121 92 52 626 66 571 98 65
Character n d h o s -s -o -h s h o w t h a t t h e y a
Milliseconds 107 58 79 81 105 90 226 153 164 327 41 74 101 70 85 57 60 87 49 106 6 152 43 107 42
Character r e c l o s e l y r e l a t e d t o t h e
Milliseconds 54 95 71 276 77 154 48 40 162 254 158 141 55 101 142 68 65 156 58 170 90 91 52 85 68
Character s l o p e o f a c u r v e a t a p o
Milliseconds 58 134 56 473 112 84 87 115 42 71 297 101 193 216 82 215 100 95 139 98 134 436 114 154 74
Character i n t P - -P P o n t h e c u r v e . W
Milliseconds 227 95 45 225 101 410 132 72 185 125 87 85 108 47 77 98 48 155 114 102 293 69 114 119 732
Character e g i e p -p - -e -i -g g i v e p r e c i s e
Milliseconds 230 86 214 97 134 70 125 368 151 161 197 168 321 131 80 65 81 66 82 63 483 125 75 55 94
Character d e v e l o p m e n t s o f t h e s e i m p
Milliseconds 258 136 106 111 64 170 89 151 118 104 66 101 80 81 106 72 99 116 72 140 83 82 338 83 128
Character o r t n -n -i -m -p -o -r -t i m p o r t a n t c o n e
Milliseconds 50 66 95 176 879 446 0 0 0 0 0 307 69 157 95 94 109 117 104 58 89 145 73 79 120
Character -e -n -o -c c o n c e p t s i n t h e n e x t
Milliseconds 390 330 156 154 230 72 66 197 144 68 110 94 87 218 46 119 65 93 52 63 102 39 221 90 82
Character c h a p t e r , u -u b u t f o r n o w w e
Milliseconds 270 97 95 84 67 103 89 75 70 242 601 119 124 104 88 457 117 77 84 66 64 44 75 165 74
Character u s e a n i n f o r m a l a p p r o a c h
Milliseconds 90 128 66 52 87 165 112 102 130 62 69 94 84 98 83 140 87 101 152 131 397 169 195 159 85
Character , s o -o -s - -, s o y o u w i l l s e e
Milliseconds 162 120 113 117 234 155 160 155 85 50 91 217 0 88 93 81 25 80 306 153 143 66 73 203 91
Character h o w t h e y l e a d n a t u r a l l y t
Milliseconds 64 51 45 96 181 96 49 102 63 109 49 75 120 70 94 82 61 85 104 66 54 177 140 97 145
Character o t h e m a i n i d e a o f t h i s c
Milliseconds 67 120 61 68 120 47 197 88 86 72 47 139 76 176 70 64 172 83 79 112 59 57 122 41 170
Character h a p t e , - -, r , t h e l i m i t . T h
Milliseconds 105 89 128 92 119 124 136 318 154 118 103 72 98 123 71 74 444 74 108 122 141 93 184 196 265
Character e i d e a o f a m i l -l -i -m l i m i t p
Milliseconds 88 28 131 66 154 64 63 93 104 39 103 140 150 71 198 299 163 159 550 75 143 132 102 94 88
Character l a y s a f o u n d a t i o n a l r o l e
Milliseconds 79 123 177 101 61 580 108 112 71 60 150 554 120 74 90 79 72 77 110 70 79 268 188 48 57
Character t h r o u g h o u t c a l c u l u s .
Milliseconds 136 102 91 91 24 82 114 104 80 29 81 230 121 74 120 72 613 264 114 48
WPM Timing
Seconds WPM
2.82 68.2
5.63 83.12
8.45 92.36
11.26 83.12
14.08 85.25
16.89 88.1
19.71 85.25
22.52 77.26
25.34 75.31
28.15 74.6
30.97 78.67
33.78 77.44
36.6 75.09
39.41 77.64
42.23 74.46
45.04 69.8
47.86 65.7
50.67 63.94
53.49 62.59
56.3 63.3
59.12 66.17
61.93 68.01
64.75 67.65
67.56 68.38
70.38 68.37
73.19 68.86
76.01 69.31
78.82 67.75
81.64 69.82
84.45 69.34
87.27 69.3
90.08 70.34
92.9 71.43
95.71 71.59
98.53 71.61
101.34 70.81
104.16 70.51
106.97 71.01
109.79 70.28
112.6 69.7
115.42 70.08
118.23 71.15
121.05 70.58
123.86 71.59
126.68 72.85
129.49 73.21
132.31 73.65
135.12 73.18
137.94 73.34
140.75 73.66