hot (hotsingle)

Race #1095

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Official speed 72.20 wpm (143.60 seconds elapsed during race)
Without ending ping 72.31 wpm (217 ms delay sending score to TypeRacer’s server)
Timerless 72.32 wpm (23 ms elapsed before first character typed; 143.36 seconds elapsed during race)
Timerless minus one 72.24 wpm, ignoring the first character typed
Race Start September 22, 2023 8:32:43am UTC
Race Finish September 22, 2023 8:35:06am UTC
Outcome No win (2 of 4)
Opponents 1. ziziaziz (92.93 wpm)
3. krishna_4241 (60.06 wpm)
Accuracy 95.9%
Points 194.94
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 CAalculus is a tool that helps us understand how a change in one wuaquanitity si is related to a change in another. How does the speed o f f a falling hobject change as a fucntnction of time> ? How does the level of waerter in a barrele change as a function of the amount of liquid poured intoo i it? EWwWWe see cahnahange coccurring in neartlyly everrythything we observe int he the world nad and universe, and powerful modern instruments help us sseee more and more. In this section we introduce the ideas of average and instanataneous rates of fchange, and hsowshow that they are closelyt related to the slope of a curve as t a point P on the curve,. We give precise developemments of these important concepts i nthe n the nedxt chapter, but for now we use an informal approach so you will wssee how they lead natrurally to the mianain idea o ff this chapter, the limit. The ideaof of a limit plays a foundational role throughout calculus.
Timing
Character C A -A a l c u l u s i s a t o o l t h a t
Milliseconds 23 384 706 127 92 193 258 148 197 136 104 65 129 431 127 118 170 95 147 141 81 218 67 87 84
Character h e l p s u s u n d e r s t a n d h o w
Milliseconds 107 110 70 102 200 50 139 324 117 120 171 167 66 182 154 184 173 137 103 71 127 79 128 50 135
Character a c h a n g e i n o n e w u a -a -u -w q u a
Milliseconds 92 142 185 96 104 135 110 138 95 95 145 54 108 149 40 81 146 122 97 283 149 123 196 113 185
Character n i -i t i t y s i - -i -s i s r e l a t e d
Milliseconds 125 183 417 190 103 89 179 135 129 15 154 337 143 113 260 148 55 494 147 121 188 143 138 194 72
Character t o a c h a n g e i n a n o t h e r . H
Milliseconds 139 44 73 170 128 437 87 83 106 90 151 97 85 89 83 135 48 117 60 84 119 176 130 65 201
Character o w d o e s t h e s p e e d o f - -f -
Milliseconds 111 437 146 213 115 80 160 72 149 48 93 54 123 96 164 154 176 55 90 127 65 161 260 146 118
Character f a f a l l i n g h -h o b j e c t c h a n
Milliseconds 104 90 86 137 141 116 245 146 151 146 219 196 134 773 311 364 347 163 184 198 99 221 74 84 103
Character g e a s a f u c n t -t -n -c n c t i o n o f
Milliseconds 76 542 150 146 220 40 211 29 180 163 104 96 170 232 182 111 221 96 175 52 141 146 90 147 8
Character t i m e > - -> ? H o w d o e s t h e l
Milliseconds 251 85 368 198 119 278 269 253 173 285 230 201 142 62 142 142 85 126 166 61 120 75 72 66 83
Character e v e l o f w a e r -r -e t e r i n a b a
Milliseconds 105 180 141 114 41 167 37 98 132 161 201 207 182 140 82 123 144 130 59 115 79 55 159 107 126
Character r r e l e - -e c h a n g e a s a f u n c
Milliseconds 104 194 148 107 106 88 282 144 167 76 101 93 156 139 172 81 120 151 123 102 154 155 109 162 57
Character t i o n o f t h e a m o u n t o f l i q
Milliseconds 200 59 149 128 21 139 37 237 86 109 60 86 113 44 127 138 161 88 103 48 154 82 103 168 153
Character u i d p o u r e d i n t o o i -i - -o i t ?
Milliseconds 92 320 287 126 193 218 180 114 110 195 119 22 113 88 59 44 122 118 324 161 124 139 136 167 329
Character E W w -w -W W -W -E W e s e e c a h n -n -h -a a -a
Milliseconds 143 370 7 115 236 162 190 271 158 234 206 282 112 176 200 30 252 118 33 181 279 152 130 410 421
Character h a n g e c -c o c c u r r i n g i n n e a r
Milliseconds 236 119 92 124 146 123 315 318 226 125 152 80 128 310 122 178 69 106 84 128 16 219 183 160 137
Character t l y -y -l -t l y e v e r r y t h -h -t -y -r y t h i
Milliseconds 17 79 169 163 163 118 194 57 111 133 183 182 70 44 114 122 82 254 152 154 112 255 204 77 170
Character n g w e o b s e r v e i n t h e -e -h - -t
Milliseconds 470 151 135 188 117 145 113 163 131 125 169 210 133 100 66 153 67 6 151 67 239 160 132 116 140
Character t h e w o r l d n a d - -d -a -n a n d u n i
Milliseconds 119 99 105 88 137 40 165 23 190 130 121 36 152 52 259 143 145 118 199 94 75 90 95 190 149
Character v e r s e , a n d p o w e r f u l m o d e r
Milliseconds 108 157 152 129 130 125 117 107 66 85 94 134 184 78 74 143 209 105 119 106 197 231 124 180 162
Character n i n s t r u m e n t s h e l p u s s s e
Milliseconds 130 72 194 162 85 154 165 66 208 18 863 182 208 131 134 101 97 214 104 157 109 99 144 111 210
Character -e -s e e m o r e a n d m o r e . I n t h
Milliseconds 285 143 108 162 104 103 98 57 106 116 98 42 95 95 154 138 91 96 194 66 257 178 132 143 45
Character i s s e c t i o n w e i n t r o d u c e t
Milliseconds 119 47 134 130 171 184 191 60 106 141 8 115 123 114 123 160 29 234 20 538 90 137 165 116 112
Character h e i d e a s o f a v e r a g e a n d i
Milliseconds 43 95 99 317 109 173 186 151 139 52 105 140 86 191 197 85 239 171 177 95 111 57 128 72 284
Character n s t a n a -a t a n e o u s r a t e s o f f
Milliseconds 141 74 142 108 116 341 541 115 135 121 252 98 151 120 92 205 155 105 164 179 84 21 118 123 133
Character -f c h a n g e , a n d h s o w -w -o -s -h s h o w
Milliseconds 402 130 107 99 126 94 146 121 91 77 130 0 118 131 55 139 103 251 148 141 108 146 111 145 73
Character t h a t t h e y a r e c l o s e l y t -
Milliseconds 103 106 63 88 100 115 90 114 85 117 57 129 140 123 96 122 80 157 74 181 98 132 6 109 289
Character -t r e l a t e d t o t h e s l o p e o f
Milliseconds 137 115 125 129 71 160 143 160 173 110 113 70 100 75 110 61 250 95 99 166 155 94 103 80 50
Character a c u r v e a s - -s t a p o i n t P
Milliseconds 123 67 133 175 75 125 188 129 122 103 168 66 280 160 91 94 82 158 115 220 171 145 138 153 171
Character o n t h e c u r v e , -, . W e g i v e
Milliseconds 174 130 137 47 129 61 85 54 175 78 129 261 176 102 371 209 119 151 193 152 207 42 163 150 68
Character p r e c i s e d e v e l o p e m -m -e m e n t s
Milliseconds 110 96 128 175 105 84 170 115 276 191 174 141 65 171 171 339 102 218 126 201 80 119 65 135 73
Character o f t h e s e i m p o r t a n t c o n c e p
Milliseconds 78 62 114 115 50 167 206 155 121 90 153 162 185 192 210 146 156 28 177 107 89 110 99 146 790
Character t s i n t h e - -e -h -t -n - n t h e n e d
Milliseconds 276 151 102 85 147 9 97 125 42 46 278 153 131 122 135 92 258 116 126 74 83 59 149 105 205
Character -d x t c h a p t e r , b u t f o r n o w
Milliseconds 429 138 197 153 93 104 71 93 179 156 168 127 72 337 106 116 111 99 87 112 64 87 131 47 169
Character w e u s e a n i n f o r m a l a p p r o a
Milliseconds 151 160 138 180 111 138 100 102 40 115 134 143 70 85 112 105 91 71 112 101 112 160 106 91 133
Character c h s o y o u w i l l w s -s -w s e e h o
Milliseconds 130 78 116 155 108 85 183 131 88 45 111 61 197 128 66 97 191 210 129 122 108 150 111 66 199
Character w t h e y l e a d n a t r -r u r a l l y t
Milliseconds 74 158 120 53 162 45 185 107 108 196 90 159 140 157 171 309 294 200 56 149 70 156 60 110 132
Character o t h e m i a n -n -a -i a i n i d e a o f
Milliseconds 82 86 101 72 91 76 98 153 83 154 242 312 140 179 72 185 42 154 63 176 211 23 153 66 207
Character -f - f t h i s c h a p t e r , t h e l i m
Milliseconds 297 130 59 60 154 54 157 119 63 187 77 60 104 85 166 167 105 87 165 50 104 87 78 135 571
Character i t . T h e i d e a o f -f -o o f a l i m
Milliseconds 209 181 392 138 235 190 109 89 106 103 180 182 153 199 262 144 193 149 153 110 62 150 74 162 165
Character i t p l a y s a f o u n d a t i o n a l r
Milliseconds 162 75 73 108 206 35 274 119 149 94 125 111 61 113 199 55 189 141 50 109 127 109 34 165 141
Character o l e t h r o u g h o u t c a l c u l u s .
Milliseconds 55 157 84 82 134 144 47 111 140 78 120 126 137 46 67 277 120 45 97 188 166 428 149 81
WPM Timing
Seconds WPM
2.87 45.96
5.74 68.94
8.62 77.99
11.49 71.03
14.36 66.02
17.23 71.03
20.1 73.42
22.98 72.07
25.85 68.24
28.72 67.27
31.59 66.47
34.46 67.2
37.34 68.46
40.21 68.64
43.08 71.31
45.95 71.29
48.82 68.33
51.7 66.39
54.57 65.53
57.44 65.6
60.31 64.46
63.18 64.38
66.06 64.49
68.93 65.63
71.8 65.51
74.67 65.89
77.54 67.01
80.42 67.75
83.29 68.29
86.16 68.11
89.03 68.6
91.9 68.81
94.78 69.26
97.65 69.92
100.52 70.19
103.39 70.22
106.26 69.79
109.14 70.59
112.01 69.96
114.88 69.46
117.75 70.11
120.62 71.03
123.5 71.22
126.37 71.31
129.24 71.31
132.11 71.48
134.99 71.47
137.86 71.29
140.73 71.97
143.6 72.2