Jack (touvski)

Race #14426

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Official speed 79.35 wpm (130.66 seconds elapsed during race)
Without ending ping 79.52 wpm (282 ms delay sending score to TypeRacer’s server)
Timerless 79.79 wpm (441 ms elapsed before first character typed; 129.94 seconds elapsed during race)
Timerless minus one 79.70 wpm, ignoring the first character typed
Race Start May 5, 2025 2:34:52pm UTC
Race Finish May 5, 2025 2:37:03pm UTC
Outcome No win (3 of 5)
Opponents 1. mrsthornton09 (90.10 wpm)
4. nbl_86 (70.42 wpm)
Accuracy 96.3%
Points 214.25
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 caqualntity its related to a change in another. How coedoes the speed ofa a falling object change as a functin oon of time? How does the level of water in a barrel change as a funciton functino on of the amount of liquid poured into it? We see change cooccuring ring in nearly everything we observe in the owrldworld and universe, and powerful modern instrumetnsnts help us see more and more. In this section we introduce the ideas of average and instantaneous rates of change, and hwoshow that they are closely related to the slpe ope of a curve at a onitpoint P on the curve. We give precise develeeopopments of these ijmpoimmporportant conceopts in the next chapter, but for now we use an ifnorinfomrmal, approach so you weill see how they lead naturally to the main idea of this chapter, the litmilimit. The iedea of a limit plays a foundattioional role throughout claalculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 441 117 105 212 90 150 115 99 95 123 126 102 204 51 199 91 144 162 20 191 55 51 82 16 101
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 83 101 115 117 71 201 94 89 523 145 38 194 83 96 89 83 60 91 104 194 73 83 51 122 88
Character c h a n g e i n o n e c a -a -c q u a l -l n t
Milliseconds 117 88 73 100 27 134 46 131 52 98 167 44 74 99 274 110 288 135 93 133 84 79 532 200 100
Character i t y i t -t s r e l a t e d t o a c h a
Milliseconds 84 132 146 110 145 111 478 67 89 172 84 161 66 100 100 183 118 121 56 72 105 95 183 89 79
Character n g e i n a n o t h e r . H o w c o e -e -o
Milliseconds 88 66 74 71 94 101 67 116 107 88 60 106 28 83 134 166 228 99 86 105 176 79 120 314 154
Character -c d o e s t h e s p e e d o f a - -a a
Milliseconds 151 73 171 67 56 95 215 67 78 35 153 74 72 159 156 96 88 77 189 106 484 145 94 77 87
Character f a l l i n g o b j e c t c h a n g e a s
Milliseconds 253 88 84 144 55 92 77 43 129 137 223 72 172 106 55 306 50 61 116 30 110 66 128 73 121
Character a f u n c t i n o -o - -n o n o f t i m e ?
Milliseconds 97 98 130 86 178 56 122 29 105 105 101 406 154 144 217 45 111 95 66 91 176 40 60 45 244
Character H o w d o e s t h e l e v e l o f w a
Milliseconds 155 289 134 77 124 127 66 100 62 99 178 99 78 36 110 77 255 125 88 121 99 53 81 411 123
Character t e r i n a b a r r e l c h a n g e a s
Milliseconds 106 95 115 139 134 111 139 34 105 144 128 205 223 611 145 106 122 93 17 150 34 105 106 95 116
Character a f u n c i t o n -f -u -n -c -i -t -o -n - f u n c
Milliseconds 106 110 95 128 111 166 45 145 16 67 39 128 432 0 0 0 0 0 0 0 0 534 112 171 89
Character t i n o - -o -n o n o f t h e a m o u n t
Milliseconds 151 0 132 67 39 507 149 156 217 29 93 132 45 91 164 45 51 66 139 89 155 85 178 348 90
Character o f l i q u i d p o u r e d i n t o i t ?
Milliseconds 161 94 44 106 85 300 60 50 319 108 185 65 96 123 187 246 82 268 104 56 77 95 94 86 219
Character W e s e e c h a n g e c o -o -c o c c u r i
Milliseconds 123 189 123 90 131 67 196 49 211 107 54 134 11 100 89 165 134 333 123 233 113 170 100 128 85
Character n g - -g -n -i r i n g i n n e a r l y e v e
Milliseconds 89 60 95 421 156 162 160 179 88 50 89 105 95 77 67 266 96 83 50 100 128 89 160 146 138
Character r y t h i n g w e o b s e r v e i n t h e
Milliseconds 95 127 139 83 53 175 50 90 161 61 144 395 110 172 91 71 284 94 124 104 73 96 274 74 51
Character o w r l d -o -w -r -l -d w o r l d a n d u n i v
Milliseconds 72 143 5 106 95 72 427 0 0 0 0 208 76 117 77 133 90 128 56 60 74 226 178 66 44
Character e r s e , a n d p o w e r f u l m o d e r n
Milliseconds 167 78 118 72 110 133 190 79 43 94 117 45 61 44 55 206 100 73 115 229 96 95 187 83 72
Character i n s t r u m e t n s -s -n -t n t s h e l p u
Milliseconds 134 138 56 139 61 172 73 177 45 122 22 150 405 151 156 218 59 63 77 288 94 61 57 99 322
Character s s e e m o r e a n d m o r e . I n t
Milliseconds 63 82 261 45 211 111 122 50 67 56 89 79 98 78 45 127 68 84 50 120 123 184 121 55 163
Character h i s s e c t i o n w e i n t r o d u c e
Milliseconds 55 45 50 60 399 63 178 160 55 57 49 78 305 79 100 176 368 177 519 94 143 106 96 216 77
Character t h e i d e a s o f a v e r a g e a n d
Milliseconds 140 48 67 41 316 133 188 67 155 150 151 71 86 186 213 162 176 166 190 83 86 180 135 39 87
Character i n s t a n t a n e o u s r a t e s o f c h
Milliseconds 213 132 95 96 66 98 401 145 329 90 419 69 87 260 157 83 145 88 94 128 167 46 89 165 78
Character a n g e , a n d h w o -h -w -o s h o w t h a t
Milliseconds 61 95 112 543 129 83 95 71 50 61 156 38 39 428 0 0 139 78 61 94 34 177 68 55 74
Character t h e y a r e c l o s e l y r e l a t e d
Milliseconds 31 228 100 73 85 86 119 104 77 58 192 113 155 88 56 127 89 118 182 78 156 73 110 89 195
Character t o t h e s l p e - -e -p o p e o f a
Milliseconds 111 239 83 79 99 73 77 33 213 37 134 132 112 350 144 152 228 59 89 106 112 49 78 89 105
Character c u r v e a t a o n i t -o -n -i -t p o i n t
Milliseconds 168 132 83 200 151 94 61 201 129 89 87 155 123 11 72 494 0 0 0 291 61 71 72 79 49
Character P o n t h e c u r v e . W e g i v e p
Milliseconds 272 239 239 44 106 128 38 50 56 183 100 34 166 135 121 117 255 189 90 446 99 87 105 78 180
Character r e c i s e d e v e l e e o p -p -o -e -e o p m e n
Milliseconds 155 90 321 94 194 51 161 155 172 285 127 129 188 72 321 45 511 134 172 157 315 183 224 111 104
Character t s o f t h e s e i j m p o -i -j -m -p -o i m m
Milliseconds 84 100 150 222 89 34 178 49 61 91 104 83 296 133 54 57 71 640 0 0 0 0 377 44 39
Character p o r -r -o -p -m p o r t a n t c o n c e o -o p t s
Milliseconds 67 38 167 345 149 167 173 283 28 106 227 106 101 66 121 325 54 56 106 189 248 433 206 72 95
Character i n t h e n e x t c h a p t e r , b u t
Milliseconds 89 185 90 102 131 53 51 50 134 60 190 104 163 176 89 68 143 106 129 88 62 126 183 62 133
Character f o r n o w w e u s e a n i f n o r -i
Milliseconds 73 195 94 105 100 328 50 39 99 617 50 79 168 32 73 381 179 122 84 132 156 90 98 84 524
Character -f -n -o -r i n f o m -m r m a l , - -, a p p r o a
Milliseconds 0 0 0 0 250 65 84 106 294 505 102 88 115 79 177 256 340 133 99 102 109 151 161 100 99
Character c h s o y o u w e -e i l l s e e h o w
Milliseconds 186 126 84 199 95 94 212 100 55 94 335 104 411 240 88 168 60 133 72 194 101 740 50 60 67
Character t h e y l e a d n a t u r a l l y t o t h
Milliseconds 172 61 105 62 88 96 54 78 168 110 194 69 104 134 83 56 71 134 66 94 161 68 62 99 89
Character e m a i n i d e a o f t h i s c h a p t
Milliseconds 34 77 183 57 104 74 82 127 62 261 68 105 139 62 81 167 11 100 8 86 234 122 85 93 78
Character e r , t h e l i t m i -l -i -t -m -i l i m i t .
Milliseconds 95 82 85 99 205 61 90 57 20 63 93 106 46 425 0 0 0 0 268 154 306 107 117 132 123
Character T h e i e -e d e a o f a l i m i t p l a
Milliseconds 171 128 17 83 107 77 382 51 178 67 101 111 72 94 78 96 539 92 167 89 83 88 87 175 106
Character y s a f o u n d a t t i o -o -i -t i o n a l r
Milliseconds 72 72 124 149 105 355 101 67 177 35 98 156 951 49 50 413 148 156 227 56 95 127 91 93 161
Character o l e t h r o u g h o u t c l a -a -l a l c u l
Milliseconds 72 178 34 127 211 45 134 60 63 87 107 210 51 93 95 289 127 133 422 129 56 194 122 100 122
Character u s .
Milliseconds 101 138 155
WPM Timing
Seconds WPM
2.61 78.06
5.23 91.84
7.84 97.96
10.45 84.95
13.07 90
15.68 86.48
18.29 85.28
20.91 88.4
23.52 86.23
26.13 88.17
28.75 88.5
31.36 87.63
33.97 83.01
36.59 82.66
39.2 82.96
41.81 83.8
44.42 80.5
47.04 82.4
49.65 82.41
52.26 82.2
54.88 83.75
57.49 82.86
60.1 84.05
62.72 84.38
65.33 84.13
67.94 84.25
70.56 83.85
73.17 83.48
75.78 84.71
78.4 84.65
81.01 84.73
83.62 84.09
86.24 84.05
88.85 83.2
91.46 82.39
94.08 81
96.69 80.42
99.3 80.6
101.92 80.77
104.53 80.02
107.14 79.07
109.76 78.83
112.37 79.13
114.98 80.05
117.6 80.72
120.21 80.16
122.82 80.41
125.44 79.69
128.05 79.75
130.66 79.35