Zachary W (thefallz)

Race #8

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Official speed 73.65 wpm (140.77 seconds elapsed during race)
Without ending ping 73.76 wpm (201 ms delay sending score to TypeRacer’s server)
Timerless 73.90 wpm (271 ms elapsed before first character typed; 140.30 seconds elapsed during race)
Timerless minus one 73.81 wpm, ignoring the first character typed
Race Start August 21, 2024 3:31:41pm UTC
Race Finish August 21, 2024 3:34:02pm UTC
Outcome No win (4 of 4)
Opponents 1. arjunprogramming (87.44 wpm)
Accuracy 94.5%
Points 198.86
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 Calcuslus is a tool that helps us understand how a change in one rquanity tity is related to a change in another. How does the speed of a faillilling onbjecobehectkjecject change as a functoion of time? How does the level of water in a barrel change as a function of the amoujntnt opf f liquid opoured inbtoito it ? wEwEWe see change occouring ring in reaneral arly everyhtithing we bobeseserve in the world oand muniverse, and cpowerful morderdern intstruments help us sshee howmmore and more. In this csectiong sintwewwe introuducde e the iddeas of average and instatnnt anoeous rates of achange ,, and show that they are closely related dt to the slope of a curve a tt a point P on the curve. We give precsissidise develpoopments of these important concepts in the next chapter, but for now we use an informal apporcroach so you will se e ee how they lead naturall.y t.y to the main idea of this chapter, the limit. The idedaa of a limit plays a foundation al role throughtoout calculus.
Timing
Character C a l c u s -s l u s i s a t o o l t h a t
Milliseconds 271 71 95 113 160 111 363 126 177 73 45 136 80 58 94 138 22 96 146 110 90 64 121 69 64
Character h e l p s u s u n d e r s t a n d h o w
Milliseconds 82 198 48 42 143 79 58 120 102 200 195 125 75 117 80 104 146 63 88 73 48 160 72 104 80
Character a c h a n g e i n o n e r -r q u a n i t y
Milliseconds 46 91 55 105 70 57 96 56 38 83 119 88 113 143 110 64 122 241 89 78 96 72 183 58 160
Character - -y -t -i t i t y i s r e l a t e d t o a
Milliseconds 70 184 135 128 129 65 81 95 136 65 150 74 55 385 70 129 103 113 30 90 56 120 46 74 369
Character c h a n g e i n a n o t h e r . H o w d
Milliseconds 112 112 102 103 33 113 63 49 88 128 84 187 106 167 121 62 99 30 120 73 358 167 123 135 127
Character o e s t h e s p e e d o f a f a i l l i
Milliseconds 79 91 45 58 110 74 71 80 95 91 93 115 101 32 80 89 57 200 465 96 87 71 151 107 197
Character -i -l -l -i l l i n g o n -n -o b j e c -c -e -j -b o b e
Milliseconds 138 129 120 133 43 168 239 126 48 48 193 354 305 119 77 128 81 63 216 129 137 134 27 200 120
Character -e h e c t -t -c -e -h k j e c -c -e -j -k j e c t c h a
Milliseconds 384 135 81 37 176 144 115 144 137 85 17 46 25 225 121 125 145 122 104 72 158 80 539 79 86
Character n g e a s a f u n c t o -o i o n o f t i
Milliseconds 34 110 48 56 104 64 97 49 97 249 61 119 88 145 153 264 129 151 142 88 138 88 31 143 58
Character m e ? H o w d o e s t h e l e v e l o f
Milliseconds 118 83 182 89 329 152 45 66 80 79 55 49 39 112 64 74 62 112 56 112 104 16 96 179 79
Character w a t e r i n a b a r r e l c h a n g e
Milliseconds 47 120 67 134 82 134 72 104 141 84 37 96 144 162 202 164 66 94 416 433 71 112 34 104 30
Character a s a f u n c t i o n o f t h e a m o
Milliseconds 66 96 78 72 112 96 203 94 121 88 150 42 136 169 86 311 96 32 144 72 80 74 96 88 176
Character u j n t -t -n -j n t o p f - -f -p f l i q u i d
Milliseconds 143 57 70 138 142 129 121 166 64 33 128 10 53 33 231 104 146 185 22 143 187 101 112 130 112
Character o -o p o u r e d i n b t o i -i -o -t -b t o i t
Milliseconds 104 318 443 69 186 209 133 427 117 50 151 144 15 50 150 16 192 137 129 360 104 14 160 130 54
Character - ? w E -E -w w E -E -w W e s e e c h a n g e
Milliseconds 41 208 481 149 122 337 247 129 134 298 103 151 113 233 112 151 175 153 74 104 72 93 40 88 49
Character o c c o -o u r i n g - -g -n -i r i n g i n r
Milliseconds 39 177 199 154 225 343 142 98 73 141 66 47 346 125 122 136 54 120 137 65 31 143 130 72 104
Character e a -a -e -r n e r a l - -l -a -r a r l y e v e r y
Milliseconds 64 24 208 118 115 192 54 63 65 103 56 296 145 105 144 62 80 88 178 62 280 90 55 127 194
Character h t i -i -t -h t h i n g w e b -b o b e s e -e -s -e
Milliseconds 134 33 136 242 111 128 64 127 49 128 54 56 122 176 209 125 274 106 76 75 141 250 246 120 136
Character s e r v e i n t h e w o r l d o -o a n d
Milliseconds 24 186 334 256 66 88 297 133 75 62 82 31 87 87 98 48 96 64 54 136 202 233 62 185 94
Character m -m u n i v e r s e , a n d c -c p o w e r f u
Milliseconds 194 314 148 136 178 110 64 136 176 131 77 123 233 92 74 72 103 282 77 160 65 135 154 152 97
Character l m o r d e r -r -e -d -r d e r n i n t -t s t r u
Milliseconds 166 73 142 137 57 105 165 48 170 118 112 106 72 119 79 154 81 149 128 290 319 71 112 130 80
Character m e n t s h e l p u s s s h -h -s e e h o w
Milliseconds 246 115 63 86 58 62 296 129 8 264 327 106 175 87 121 120 183 202 129 71 648 70 104 122 104
Character -w -o m -m -h m o r e a n d m o r e . I n t h
Milliseconds 192 126 235 189 120 154 142 40 26 40 166 104 66 47 106 135 48 24 137 149 218 208 63 71 41
Character i s c -c s e c t i o n g - -g s -s i n t -t -n w
Milliseconds 151 66 55 105 254 98 128 56 175 75 110 184 97 103 200 120 113 336 207 150 146 79 282 120 77
Character e -e -w w -w -i w e i n t r o u -u d u c d e - -e -d
Milliseconds 184 67 112 215 176 118 96 34 78 411 119 80 120 64 142 280 96 120 99 167 168 46 274 118 115
Character e t h e i d d -d e a s o f a v e r a g e
Milliseconds 109 16 226 88 70 64 129 9 113 328 96 85 74 111 192 81 46 185 199 16 162 176 105 39 78
Character a n d i n s t a t n -n -t n t - a n o -o e o u s
Milliseconds 179 112 53 72 99 333 122 271 216 64 225 294 113 193 47 78 347 86 153 185 288 79 74 157 82
Character r a t e s o f a -a c h a n g e , -, - , a
Milliseconds 56 261 43 141 50 143 170 216 72 46 200 283 84 80 67 73 76 26 62 203 176 118 90 56 102
Character n d s h o w t h a t t h e y a r e c l o
Milliseconds 127 75 53 80 89 151 68 38 113 80 64 39 89 262 82 55 96 89 37 105 41 62 171 80 120
Character s e l y r e l a t e d d t - -t -d t o t h e
Milliseconds 54 143 227 118 72 263 51 190 90 119 48 105 55 46 177 23 250 129 109 243 69 80 83 117 113
Character s l o p e o f a c u r v e a t -t - t
Milliseconds 160 83 53 112 241 145 64 118 80 57 71 75 127 256 38 195 13 42 413 60 207 264 120 144 62
Character a p o i n t P o n t h e c u r v e . W
Milliseconds 73 81 88 728 159 150 66 38 267 125 258 152 71 82 72 54 87 154 209 71 158 50 87 106 231
Character e g i v e p r e c s i s -s -i -s s i d -d -i -s i s
Milliseconds 190 84 87 62 88 47 83 142 104 88 570 62 104 114 255 128 135 71 82 71 273 126 139 53 64
Character e d e v e l p o -o -p o p m e n t s o f t h e
Milliseconds 58 106 263 143 81 78 50 176 200 208 135 145 381 299 88 80 70 39 65 216 63 51 159 65 101
Character s e i m p o r t a n t c o n c e p t s i n
Milliseconds 154 136 81 253 145 169 142 67 125 83 110 66 64 406 72 176 160 59 126 151 74 71 247 154 54
Character t h e n e x t c h a p t e r , b u t f o r
Milliseconds 74 104 63 80 120 16 160 190 97 377 78 146 112 72 32 111 114 88 325 88 98 62 112 83 70
Character n o w w e u s e a n i n f o r m a l a
Milliseconds 66 197 465 50 37 272 144 80 114 70 42 46 155 111 113 253 123 86 87 146 103 178 176 88 240
Character p p o r c -c -r -o r o a c h s o y o u w i l l
Milliseconds 222 119 152 59 206 151 131 143 202 84 121 12 150 63 218 87 121 191 72 70 74 104 47 134 106
Character s e - -e e e -e - e h o w t h e y l e a
Milliseconds 64 30 177 97 238 131 71 33 358 248 127 113 209 91 100 113 79 129 81 62 55 57 227 111 62
Character d n a t u r a l l . y - -y -. t . -. -t y t o
Milliseconds 106 78 138 279 238 99 121 92 42 112 201 45 80 291 125 123 224 25 318 128 71 71 380 95 65
Character t h e m a i n i d e a o f t h i s c h a
Milliseconds 87 87 96 88 112 103 71 121 66 143 71 137 71 63 235 62 65 105 72 135 64 46 104 107 61
Character p t e r , t h e l i m i t . T h e i d e d
Milliseconds 153 72 33 104 128 102 313 80 65 80 256 134 138 118 88 128 113 256 120 153 89 85 90 174 27
Character a -a -d a o f a l i m i t p l a y s a f
Milliseconds 29 313 137 320 96 134 59 38 169 89 125 154 121 133 75 55 168 128 73 86 120 49 264 552 152
Character o u n d a t i o n - a l r o l e t h r o u g
Milliseconds 89 141 113 72 98 190 42 112 150 98 256 158 87 98 350 129 143 83 37 194 193 176 71 158 107
Character h t o -o -t o u t c a l c u l u s .
Milliseconds 78 135 139 303 126 80 170 47 41 208 56 79 199 404 189 176 65 174
WPM Timing
Seconds WPM
2.82 89.51
5.63 104.42
8.45 96.61
11.26 96.96
14.08 99.73
16.89 95.19
19.71 85.85
22.52 77.25
25.34 78.14
28.15 83.11
30.97 84.08
33.79 85.6
36.6 83.93
39.42 82.2
42.23 78.99
45.05 77.78
47.86 75.97
50.68 74.11
53.49 73.58
56.31 72.88
59.13 72.86
61.94 72.84
64.76 72.46
67.57 71.57
70.39 71.6
73.2 71.47
76.02 69.46
78.83 69.26
81.65 69.96
84.46 68.9
87.28 69.16
90.1 70.99
92.91 71.04
95.73 71.33
98.54 71.6
101.36 71.86
104.17 70.96
106.99 71.22
109.8 71.91
112.62 72.56
115.43 72.98
118.25 72.76
121.07 72.56
123.88 72.75
126.7 72.74
129.51 73.57
132.33 73.64
135.14 73.88
137.96 73.94
140.77 73.65