Abhi (uhsizeal)

Race #1408

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Official speed 71.86 wpm (144.28 seconds elapsed during race)
Without ending ping 71.90 wpm (78 ms delay sending score to TypeRacer’s server)
Timerless 72.25 wpm (696 ms elapsed before first character typed; 143.51 seconds elapsed during race)
Timerless minus one 72.16 wpm, ignoring the first character typed
Race Start December 5, 2023 12:18:07am UTC
Race Finish December 5, 2023 12:20:31am UTC
Outcome No win (3 of 5)
Opponents 1. spectacularcommodity (101.05 wpm)
2. rufusdusol (98.90 wpm)
Accuracy 98.2%
Points 194.03
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 does the speed of a falling object change as a func titions of ot tf time? How does the level of water in ab abarrel change as a function of the amount of lqiquuid poured into it? We see change occurring in neeararly everything we observe in the world and universe, and pwoerowerful modern instruments help us see more and more. In this section we introduce theide ideas of average and instanteaneous rates of change, and show that they ae re closely related to the slope of a curve at a point P on the curve. We give precidse developments of these important concepts in the next chapter, but for now we use an informal approach so you will swee how they lead naturally to the main iaddea of this chapter, the limit. The idea of a limit plays a foundational role throughtouout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 696 224 160 911 113 159 243 94 130 145 64 95 465 111 157 116 128 223 126 96 83 77 130 64 176
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 128 80 208 112 64 190 65 97 144 144 63 178 125 178 145 127 95 98 79 144 144 64 78 114 144
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 128 78 81 80 111 130 94 98 128 78 145 111 66 95 209 97 159 64 160 112 160 100 507 178 93
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 83 143 110 144 66 126 128 178 128 128 80 126 51 205 179 79 112 111 111 146 95 113 112 193 189
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 96 130 17 109 33 161 128 110 291 159 160 224 142 100 95 158 114 127 80 81 32 142 80 144 159
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 176 117 107 96 163 188 163 144 173 164 143 593 127 64 110 384 242 223 113 142 192 100 188 115 79
Character n g e a s a f u n c t i -i -t - t i o n s
Milliseconds 79 50 161 93 111 242 128 112 160 174 195 173 120 0 155 12 353 192 163 125 99 157 112 112 97
Character o f - -f -o - -s o t t -t - -t f t i m e ? H
Milliseconds 161 32 126 306 158 146 160 161 368 221 579 144 223 275 157 206 179 175 158 98 128 48 590 130 302
Character o w d o e s t h e l e v e l o f w a t e
Milliseconds 130 78 437 109 128 93 178 144 96 97 63 64 190 67 190 162 95 112 129 30 147 287 159 177 145
Character r i n a b - -b a -a b a r r e l c h a n g
Milliseconds 126 97 112 109 432 99 223 112 462 147 190 191 436 126 161 192 143 161 142 160 258 81 62 114 62
Character e a s a f u n c t i o n o f t h e a m
Milliseconds 144 97 126 226 654 115 174 142 115 175 112 160 47 192 67 64 126 78 66 112 78 48 81 161 143
Character o u n t o f l q -q i q u u -u i d p o u r e d
Milliseconds 162 113 143 13 98 142 98 81 205 16 547 367 302 131 335 495 194 64 93 226 209 111 419 155 195
Character i n t o i t ? W e s e e c h a n g e o
Milliseconds 128 160 175 32 128 127 143 48 400 146 303 257 142 196 174 161 96 126 64 98 93 114 178 110 257
Character c c u r r i n g i n n e e a r -r -a -e a r l y
Milliseconds 125 146 111 82 400 159 95 83 92 179 112 80 639 112 879 192 159 323 159 210 365 207 112 163 159
Character e v e r y t h i n g w e o b s e r v e i n
Milliseconds 321 175 144 127 95 148 79 127 113 48 109 211 175 129 240 176 573 234 135 226 160 143 209 127 65
Character t h e w o r l d a n d u n i v e r s e , a
Milliseconds 46 178 29 98 240 111 63 147 80 95 209 128 113 94 192 161 144 93 162 127 192 290 158 99 158
Character n d p w o e r -r -e -o -w o w e r f u l m o d e r
Milliseconds 96 95 65 337 95 96 128 162 319 173 112 179 256 65 204 192 258 96 238 259 240 189 112 177 130
Character n i n s t r u m e n t s h e l p u s s e e
Milliseconds 189 100 220 146 81 400 224 319 209 17 142 33 192 237 195 94 114 239 96 145 97 79 176 175 142
Character m o r e a n d m o r e . I n t h i s s
Milliseconds 98 129 144 46 146 80 128 111 47 95 82 161 34 139 99 80 302 130 97 77 98 125 82 82 159
Character e c t i o n w e i n t r o d u c e t h e i d
Milliseconds 159 192 176 47 193 95 82 272 208 176 173 98 65 221 130 193 110 113 177 126 114 96 64 159 97
Character e -e -d -i i d e a s o f a v e r a g e a n d
Milliseconds 176 318 161 175 210 301 81 162 192 238 147 144 79 80 79 225 189 352 146 162 126 112 208 128 46
Character i n s t a n t e -e a n e o u s r a t e s o f
Milliseconds 48 147 125 64 194 142 97 210 175 545 78 145 302 211 126 97 145 333 194 176 144 192 113 285 403
Character c h a n g e , a n d s h o w t h a t t h
Milliseconds 144 157 96 82 462 114 144 288 112 113 95 111 64 131 76 162 79 143 144 83 65 108 114 126 99
Character e y a e - -e r e c l o s e l y r e l a t e
Milliseconds 109 83 127 176 242 191 416 174 82 144 384 288 129 175 81 239 143 161 111 114 111 352 144 192 113
Character d t o t h e s l o p e o f a c u r v e
Milliseconds 192 112 111 81 113 47 127 32 62 162 62 259 589 114 158 176 84 63 189 131 174 146 80 303 145
Character a t a p o i n t P o n t h e c u r v
Milliseconds 112 109 178 110 162 97 159 193 143 128 46 114 208 222 416 115 64 64 96 63 32 304 94 96 273
Character e . W e g i v e p r e c i d -d s e d e v e
Milliseconds 161 144 128 174 192 66 177 80 125 161 66 141 80 210 497 125 149 397 63 175 176 82 208 176 158
Character l o p m e n t s o f t h e s e i m p o r t a
Milliseconds 98 190 179 160 45 146 33 191 127 176 80 79 115 63 81 192 173 98 129 144 157 131 207 366 178
Character n t c o n c e p t s i n t h e n e x t c
Milliseconds 80 94 132 398 95 114 111 191 111 99 191 142 130 129 47 30 130 32 62 240 147 255 161 113 190
Character h a p t e r , b u t f o r n o w w e u s
Milliseconds 97 96 125 306 160 128 127 114 143 80 127 82 253 112 83 65 157 337 143 131 222 159 114 253 98
Character e a n i n f o r m a l a p p r o a c h s o
Milliseconds 161 95 143 161 94 226 128 81 125 98 161 113 206 129 224 79 144 94 129 82 432 127 127 305 95
Character y o u w i l l s w -w e e h o w t h e y
Milliseconds 129 176 127 98 95 65 93 210 127 146 109 259 416 109 147 126 177 144 63 114 79 81 127 128 144
Character l e a d n a t u r a l l y t o t h e m a i
Milliseconds 287 95 162 160 97 239 94 194 94 80 193 129 125 147 126 35 95 113 639 79 83 46 126 97 98
Character n i a d -d -a d e a o f t h i s c h a p t e
Milliseconds 125 96 163 79 176 366 146 608 207 161 79 129 96 64 144 65 125 48 98 146 79 95 158 320 146
Character r , t h e l i m i t . T h e i d e a o f
Milliseconds 126 146 97 94 97 46 64 176 147 126 145 64 160 82 172 130 47 65 112 112 177 671 81 127 78
Character a l i m i t p l a y s a f o u n d a t i
Milliseconds 82 128 146 140 160 144 131 48 94 177 128 79 161 286 145 114 111 160 81 111 143 32 159 162 64
Character o n a l r o l e t h r o u g h t o u -u -o -t o u
Milliseconds 144 96 94 114 128 144 78 192 35 109 144 82 448 111 113 48 143 96 226 95 288 305 191 270 130
Character t c a l c u l u s .
Milliseconds 80 94 176 194 160 416 256 160 226 92 147
WPM Timing
Seconds WPM
2.89 41.59
5.77 64.46
8.66 77.63
11.54 80.05
14.43 83.17
17.31 85.94
20.2 83.17
23.08 83.17
25.97 77.16
28.86 70.7
31.74 70.32
34.63 71.74
37.51 68.78
40.4 69.21
43.28 70.97
46.17 68.88
49.06 68.74
51.94 69.77
54.83 67.19
57.71 67.37
60.6 67.53
63.48 68.24
66.37 66.9
69.25 66.88
72.14 67.37
75.03 68.78
77.91 69.31
80.8 68.76
83.68 68.97
86.57 68.48
89.45 68.55
92.34 68.49
95.23 68.43
98.11 68.86
101 69.03
103.88 69.77
106.77 69.35
109.65 69.82
112.54 70.38
115.42 70.7
118.31 70.9
121.2 70.99
124.08 71.18
126.97 71.45
129.85 70.88
132.74 71.6
135.62 71.85
138.51 72.26
141.39 72.22
144.28 71.86