Sid (sid9437)

Race #2046

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Official speed 67.92 wpm (152.65 seconds elapsed during race)
Without ending ping 68.38 wpm (1,031 ms delay sending score to TypeRacer’s server)
Timerless 68.90 wpm (1,141 ms elapsed before first character typed; 150.48 seconds elapsed during race)
Timerless minus one 68.82 wpm, ignoring the first character typed
Race Start May 29, 2023 3:26:28pm UTC
Race Finish May 29, 2023 3:29:01pm UTC
Outcome No win (4 of 4)
Opponents 1. siftage (93.96 wpm)
2. king_vegeta (76.84 wpm)
3. ezeekey (70.11 wpm)
Accuracy 96.1%
Points 183.39
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 tollol that helps us understand how ahcanchacha change in one wquaquantitu y is related to a change in another. How does the speed of a falling objecy ct change as a function of time? GHoew sdoes the level of water in abaa barrel change as a function of the amounr t of liquid poured into it>? wWe see change occuring ring in nearly everything we obserevve in the world and universe, and powrefuerful modern instruments help us see more and more. In this section we introduce the idea s of avreerage and instantanewous raytes of ahcchange, and show that thayey are sclosely related to the slope a pof of a curve at a point P on tehe curve. We give precise dedvelopments of these important concepts in the next chapetter, but for noww wes use an informal approach so you will see how they lead naturlalrallally tot the main idea of thjis chapter, the limit. The isdea s of a limit plays a foundationa; l role throughout cacllculus.
Timing
Character C a l c u l u s i s a t o l l -l -l o l t h
Milliseconds 1141 205 126 132 149 145 199 116 57 178 105 25 566 103 137 46 147 139 342 134 230 144 156 99 68
Character a t h e l p s u s u n d e r s t a n d h o
Milliseconds 114 52 123 150 103 133 166 120 89 148 91 81 150 107 71 99 152 108 389 100 140 87 103 197 140
Character w a h c a n -n -a -c -h c h a -a -h -c -a c h -h -c a c
Milliseconds 161 20 206 195 8 246 91 213 132 166 223 547 131 144 280 149 134 137 141 129 358 134 233 112 130
Character h a n g e i n o n e w q u a -a -u -q -w q u a n
Milliseconds 64 372 121 149 78 65 125 120 158 126 123 92 67 172 7 89 121 257 159 122 1400 1211 76 130 62
Character t i t u - -u y i s r e l a t e d t o a
Milliseconds 230 156 158 220 156 419 138 248 138 158 98 60 112 153 433 145 197 71 158 89 282 7 401 112 93
Character c h a n g e i n a n o t h e r . H o w d o
Milliseconds 108 95 97 73 155 92 63 139 102 163 101 93 152 99 100 52 122 119 112 250 156 86 139 98 122
Character e s t h e s p e e d o f a f a l l i n g
Milliseconds 65 113 77 189 136 72 99 114 90 112 174 148 99 151 107 51 132 21 199 199 51 139 185 157 90
Character o b j e c y - -y -c c t c h a n g e a s a
Milliseconds 50 166 145 151 54 168 68 137 340 130 128 786 118 142 172 95 125 112 162 75 105 25 117 87 64
Character f u n c t i o n o f t i m e ? G -G H o e -e
Milliseconds 107 127 101 144 77 200 19 149 173 144 175 478 52 156 73 149 50 366 153 209 331 215 141 90 291
Character w s -s d o e s t h e l e v e l o f w a t
Milliseconds 102 108 230 248 73 108 103 312 187 100 82 131 63 163 69 164 173 139 163 148 72 81 154 158 120
Character e r i n a b a -a -b -a a b a r r e l c h a n
Milliseconds 57 172 91 119 103 152 122 105 128 333 140 149 764 98 158 82 163 312 166 114 160 94 118 80 84
Character g e a s a f u n c t i o n o f t h e a
Milliseconds 174 55 95 113 104 88 170 65 179 102 132 82 203 37 144 152 136 146 114 37 201 139 61 117 108
Character m o u n r - -r t o f l i q u i d p o u r e
Milliseconds 92 193 191 147 108 86 278 124 89 94 165 93 40 155 182 94 110 142 154 84 180 216 464 95 104
Character d i n t o i t > -> ? w -w W e s e e c h a
Milliseconds 192 98 146 108 127 83 98 180 38 363 299 353 163 290 578 367 210 115 96 174 150 100 106 98 116
Character n g e o c c u r i n g - -g -n -i r i n g i n
Milliseconds 78 173 75 79 173 94 175 91 119 71 153 93 89 226 150 147 135 223 62 150 112 261 169 109 157
Character n e a r l y e v e r y t h i n g w e o b s e
Milliseconds 160 78 212 170 60 185 133 75 104 58 147 361 128 63 167 155 62 113 103 99 170 216 203 96 197
Character r e v -v -e v e i n t h e w o r l d a n d
Milliseconds 399 410 236 247 226 143 138 55 148 102 139 65 134 50 120 100 101 90 115 121 125 97 119 47 88
Character u n i v e r s e , a n d p o w r e f u -u -f -e -r
Milliseconds 269 131 142 79 149 124 176 651 84 157 71 105 11 132 165 124 44 210 0 146 75 232 144 153 134
Character e r f u l m o d e r n i n s t r u m e n t s
Milliseconds 114 165 172 66 167 148 162 133 61 100 140 72 120 149 97 114 142 88 109 171 118 102 114 177 101
Character h e l p u s s e e m o r e a n d m o r e
Milliseconds 145 84 93 161 147 191 91 97 157 172 144 98 153 147 180 168 156 120 116 54 89 151 162 74 118
Character . I n t h i s s e c t i o n w e i n t r
Milliseconds 100 161 199 107 144 119 83 158 79 89 99 176 216 209 26 154 185 150 55 144 111 171 113 138 122
Character o d u c e t h e i d e a - s o f a v r e
Milliseconds 144 138 91 98 168 62 138 83 52 104 165 50 190 151 119 357 102 87 154 132 100 90 117 75 143
Character -e -r e r a g e a n d i n s t a n t a n e w -w o
Milliseconds 226 143 89 165 152 132 89 84 80 127 104 45 141 92 122 151 91 111 170 244 125 167 174 373 199
Character u s r a y -y t e s o f a h c -c -h -a c h a n g
Milliseconds 265 92 101 342 76 123 436 146 131 194 52 168 62 96 105 102 142 311 141 139 127 157 131 93 157
Character e , a n d s h o w t h a t t h a y -y -a e y
Milliseconds 104 78 152 45 139 10 145 108 98 152 98 72 194 135 116 87 133 185 146 117 96 333 122 88 168
Character a r e s -s c l o s e l y r e l a t e d t o
Milliseconds 160 87 151 121 70 172 279 98 61 154 34 198 67 200 123 170 92 357 173 147 79 155 93 149 101
Character t h e s l o p e a - -a p o f - -f -o -p o f
Milliseconds 141 103 130 46 139 120 113 148 149 72 99 106 157 224 133 158 11 88 110 248 124 147 132 190 84
Character a c u r v e a t a p o i n t P o n
Milliseconds 123 40 94 141 127 105 286 146 77 293 237 101 156 96 404 208 230 163 50 117 369 166 156 92 139
Character t e -e h e c u r v e . W e g i v e p r e c
Milliseconds 89 140 490 190 89 44 142 90 111 238 184 65 156 268 200 83 179 130 120 129 100 159 66 146 257
Character i s e d e d -d v e l o p m e n t s o f t h e
Milliseconds 109 174 250 73 128 93 150 460 183 153 142 267 143 161 104 125 92 160 65 152 119 16 215 82 92
Character s e i m p o r t a n t c o n c e p t s i n
Milliseconds 186 145 46 177 115 134 127 9 785 193 114 108 66 129 66 86 100 155 107 90 171 77 170 103 149
Character t h e n e x t c h a p e t -t -e t e r , b u t
Milliseconds 101 112 51 140 137 32 325 88 152 119 122 123 184 100 290 174 149 439 128 117 76 147 143 127 85
Character f o r n o w -w w w e s - -s u s e a n
Milliseconds 90 87 69 144 9 135 146 165 286 417 566 165 121 213 245 277 110 174 175 67 664 197 110 116 138
Character i n f o r m a l a p p r o a c h s o y o u
Milliseconds 141 102 54 137 58 132 78 261 201 173 119 132 363 115 218 178 136 145 82 92 128 186 159 158 121
Character w i l l s e e h o w t h e y l e a d n a
Milliseconds 115 71 153 146 160 55 195 148 49 214 139 113 61 180 126 134 47 189 163 57 139 155 77 162 84
Character t u r l a l -l -a -l r a l l -l -l -a -r a l l y t o t
Milliseconds 173 111 94 151 24 171 336 148 152 128 144 61 140 220 137 146 147 121 62 141 217 162 137 93 126
Character - -t t h e m a i n i d e a o f t h j -j
Milliseconds 33 391 123 162 93 129 14 151 141 106 95 126 162 324 279 169 137 93 137 101 57 121 353 9 657
Character i s c h a p t e r , t h e l i m i t . T h
Milliseconds 196 67 115 102 86 99 89 132 88 163 77 175 126 62 131 65 181 152 127 178 141 128 167 200 131
Character e i s -s d e a s - -s o f a l i m i t p
Milliseconds 83 111 224 137 286 45 159 140 129 123 141 315 148 398 82 62 102 65 169 158 127 142 78 82 149
Character l a y s a f o u n d a t i o n a ; - -; l r
Milliseconds 83 126 127 110 75 70 91 154 31 139 132 8 226 192 59 142 150 92 107 134 254 145 325 145 121
Character o l e t h r o u g h o u t c a c l -l -c l c u l
Milliseconds 72 147 230 156 82 88 130 111 168 149 59 157 171 89 70 173 177 152 196 235 118 178 108 252 146
Character u s .
Milliseconds 182 68 108
WPM Timing
Seconds WPM
3.05 47.17
6.11 60.92
9.16 62.89
12.21 47.17
15.27 50.31
18.32 45.2
21.37 46.04
24.42 52.57
27.48 58.08
30.53 56.6
33.58 60.39
36.64 59.29
39.69 61.38
42.74 59.8
45.8 62.36
48.85 63.38
51.9 63.81
54.95 62.67
58.01 62.48
61.06 63.87
64.11 63.08
67.17 63.96
70.22 64.09
73.27 65.51
76.33 66.5
79.38 67.58
82.43 67.69
85.48 67.94
88.54 67.36
91.59 68.13
94.64 67.96
97.7 68.42
100.75 67.77
103.8 67.63
106.86 67.94
109.91 67.69
112.96 68.09
116.01 68.89
119.07 68.84
122.12 67.8
125.17 67.97
128.23 68.41
131.28 68.37
134.33 67.62
137.39 67.69
140.44 68.19
143.49 67.82
146.54 68.54
149.6 68.58
152.65 67.92