player1 (player10987)

Race #110

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Official speed 67.05 wpm (154.63 seconds elapsed during race)
Without ending ping 67.16 wpm (258 ms delay sending score to TypeRacer’s server)
Timerless 67.57 wpm (938 ms elapsed before first character typed; 153.44 seconds elapsed during race)
Timerless minus one 67.49 wpm, ignoring the first character typed
Race Start October 11, 2023 4:25:01am UTC
Race Finish October 11, 2023 4:27:36am UTC
Outcome No win (5 of 5)
Opponents 1. slithical (117.85 wpm)
2. twillerdog (93.41 wpm)
3. rubikstyper (88.92 wpm)
Accuracy 97.1%
Points 181.04
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 heplps us nunderstand how a change in on e quantity is related to a change in another. How does the speed of a lfalling object change as a function of time>? How does the level of water in ab barrel change as a function of the amount of liquid poured into it? We see change occuiringring in nearl t y everything we obseverve in the wolrrld and universe, and pwowerful modern intrstruments help us see more and more. In this section sewe introduce the ideas of average and instantaneous rates of change, and show that they are closely related the tho th e slope of a curve at a point P on hthe curve. We give perrecise developments of these eimportant concepts in the nect chxt chapter, but for now we use and= i infrormal 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 doufoundational role throughout clalculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 938 279 170 131 135 155 189 96 144 115 97 114 85 99 140 76 125 188 226 99 103 123 61 136 101
Character e p -p l p s u s n -n u n d e r s t a n d h o
Milliseconds 103 139 306 232 315 103 119 183 79 87 299 334 264 146 83 142 133 181 95 99 98 101 58 116 151
Character w a c h a n g e i n o n - e q u a n t
Milliseconds 90 103 78 94 150 19 329 96 172 90 88 87 173 296 119 175 218 311 114 119 145 117 272 163 131
Character i t y i s r e l a t e d t o a c h a n g
Milliseconds 158 135 110 198 163 121 83 123 140 122 74 195 167 156 109 129 33 220 416 139 130 122 94 95 167
Character e i n a n o t h e r . H o w d o e s t h
Milliseconds 73 88 138 175 136 81 78 151 121 95 101 151 107 201 193 181 90 143 45 116 49 152 65 125 72
Character e s p e e d o f a l -l f a l l i n g o b
Milliseconds 110 64 159 337 147 150 301 154 112 121 110 125 92 156 316 115 176 95 110 203 132 83 92 74 185
Character j e c t c h a n g e a s a f u n c t i o n
Milliseconds 186 89 218 95 187 235 92 154 608 192 100 128 111 170 129 72 136 156 117 168 66 175 80 121 150
Character o f t i m e > -> ? H o w d o e s t h e
Milliseconds 137 138 54 154 99 80 162 117 1006 319 384 250 238 198 95 192 91 111 36 163 117 102 118 78 94
Character l e v e l o f w a t e r i n a b -b b a r
Milliseconds 142 113 152 79 148 155 255 101 129 78 179 112 69 143 71 137 161 141 89 104 554 311 593 115 255
Character r e l c h a n g e a s a f u n c t i o n
Milliseconds 133 150 111 174 198 125 94 77 179 76 111 190 150 129 77 115 90 105 152 44 181 56 136 160 144
Character o f t h e a m o u n t o f l i q u i d p
Milliseconds 126 57 164 92 106 85 121 368 102 138 204 175 39 143 87 139 119 133 191 86 233 149 129 223 1020
Character o u r e d i n t o i t ? W e s e e c h a
Milliseconds 263 294 145 145 135 92 105 224 133 129 161 122 101 438 237 529 540 177 86 129 133 91 153 118 86
Character n g e o c c u i -i r i n g -g -n -i r i n g i n
Milliseconds 81 338 74 151 228 139 106 125 156 322 90 173 163 115 239 141 163 116 221 159 91 81 105 149 197
Character n e a r l - t - -t y e v e r y t h i n g w
Milliseconds 116 87 182 186 123 242 346 119 133 287 145 118 182 112 130 51 131 105 152 96 149 164 94 111 162
Character e o b s e v e -e -v r v e i n t h e w o l r
Milliseconds 151 101 113 217 209 159 184 117 296 140 412 217 130 84 126 158 129 32 130 83 113 123 59 198 180
Character -r -l r l d a n d u n i v e r s e , a n d p
Milliseconds 365 140 128 141 111 137 130 103 106 157 620 149 126 185 61 146 169 113 165 187 50 147 70 114 136
Character w -w o w e r f u l m o d e r n i n t r -r -t s t
Milliseconds 270 304 224 48 171 184 194 126 176 200 389 471 125 146 147 275 163 220 167 120 167 472 154 839 308
Character r u m e n t s h e l p u s s e e m o r e
Milliseconds 294 163 184 99 197 110 217 193 299 107 502 194 165 146 86 109 62 141 136 67 111 148 47 157 49
Character a n d m o r e . I n t h i s s e c t i o n
Milliseconds 124 84 88 66 97 153 62 161 62 207 183 165 170 137 111 129 63 120 88 116 181 155 46 142 173
Character s e -e -s w e i n t r o d u c e t h e i d e
Milliseconds 135 51 137 317 151 97 165 100 159 148 102 145 173 339 245 154 171 178 145 112 101 87 126 125 207
Character a s o f a v e r a g e a n d i n s t a n t
Milliseconds 201 148 71 138 108 127 137 132 173 151 195 111 89 97 106 102 144 184 459 281 136 207 111 176 146
Character a n e o u s r a t e s o f c h a n g e , a
Milliseconds 466 251 157 484 471 121 202 222 192 99 87 149 36 126 40 121 98 53 139 33 190 65 189 175 64
Character n d s h o w t h a t t h e y a r e c l o
Milliseconds 124 61 136 85 71 164 84 107 88 106 301 100 157 108 88 98 86 209 144 188 148 141 242 98 157
Character s e l y r e l a t e d t h e t h -h -t - -e -h o
Milliseconds 23 152 117 161 146 171 150 160 70 201 162 168 85 100 102 88 105 70 128 235 127 138 147 153 293
Character t h - e s l o p e o f a c u r v e a
Milliseconds 166 70 126 183 273 137 186 165 99 158 134 107 131 167 240 137 157 106 156 133 91 294 107 125 100
Character t a p o i n t P o n h -h t h e c u r v
Milliseconds 141 171 335 134 170 278 228 162 81 242 236 243 122 168 132 207 286 77 197 49 135 115 105 74 186
Character e . W e g i v e p e -e r -r r e c i s e d e
Milliseconds 114 158 233 617 424 98 167 106 213 100 162 150 95 752 391 285 507 185 210 176 37 174 156 525 143
Character v e l o p m e n t s o f t h e s e e -e i m p
Milliseconds 155 79 171 196 197 252 125 193 80 201 103 114 101 111 117 181 138 178 145 99 125 458 233 166 140
Character o r t a n t c o n c e p t s i n t h e n e
Milliseconds 169 125 180 221 135 166 152 147 95 171 82 163 153 66 216 8 186 158 141 69 127 70 122 87 33
Character c t c h -h -c - -t -c x t c h a p t e r , b u t
Milliseconds 194 115 177 67 62 306 136 150 237 235 582 121 176 102 140 151 90 212 44 187 158 183 150 154 119
Character f o r n o w w e u s e a n d = i -i - -=
Milliseconds 133 117 100 108 121 139 176 129 186 112 169 78 131 89 154 37 161 157 296 313 180 151 331 146 157
Character -d i n f r -r o r m a l a p p r o a c h s o
Milliseconds 170 270 163 138 85 182 405 253 112 66 156 81 169 136 162 294 258 170 413 312 151 148 107 87 155
Character y o u w i l l s e e h o w t h e y l e a
Milliseconds 209 104 122 150 91 81 171 128 170 71 142 131 41 142 157 116 127 219 113 72 95 170 140 41 191
Character d n a t u r a l l y t o t h e m a i n i
Milliseconds 170 160 165 93 228 138 64 199 111 117 125 154 97 121 136 82 99 102 92 146 136 88 158 372 186
Character d e a o f t h i s c h a p t e r , t h e
Milliseconds 107 136 160 79 104 102 101 72 85 144 76 112 97 32 193 36 241 47 160 82 176 80 92 91 112
Character l i m i t , -, . T h e i d e a o f a l i
Milliseconds 281 191 172 152 89 181 453 239 208 229 811 125 169 147 104 139 182 190 116 221 240 112 142 144 181
Character m i t p l a y s a d o u -u -o -d f o u n d a t
Milliseconds 157 164 99 114 138 165 102 150 88 130 86 149 348 138 167 276 319 196 618 138 189 227 221 205 212
Character i o n a l r o l e t h r o u g h o u t c l -l
Milliseconds 106 114 168 262 139 172 164 102 156 84 146 149 127 136 124 147 193 160 204 185 107 118 151 435 436
Character a l c u l u s .
Milliseconds 111 146 147 116 163 472 131 423
WPM Timing
Seconds WPM
3.09 65.96
6.19 64.02
9.28 71.14
12.37 69.84
15.46 72.95
18.56 78.25
21.65 75.94
24.74 75.66
27.83 75.45
30.93 74.5
34.02 74.08
37.11 74.05
40.2 75.51
43.3 73.72
46.39 72.43
49.48 72.03
52.57 70.76
55.67 70.71
58.76 70.05
61.85 69.46
64.94 69.1
68.04 67.55
71.13 66.64
74.22 68.07
77.32 68.29
80.41 68.65
83.5 68.84
86.59 68.32
89.69 69.58
92.78 70.1
95.87 68.97
98.96 69.24
102.06 68.9
105.15 68.82
108.24 67.74
111.33 67.8
114.43 67.64
117.52 67.5
120.61 67.36
123.7 67.32
126.8 66.72
129.89 66.8
132.98 67.32
136.08 67.82
139.17 68.55
142.26 67.99
145.35 68.19
148.45 67.34
151.54 67.63
154.63 67.05