A (abcd1209)

Race #764

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Official speed 75.78 wpm (136.82 seconds elapsed during race)
Without ending ping 75.89 wpm (198 ms delay sending score to TypeRacer’s server)
Timerless 76.07 wpm (327 ms elapsed before first character typed; 136.29 seconds elapsed during race)
Timerless minus one 75.98 wpm, ignoring the first character typed
Race Start March 16, 2024 8:06:49pm UTC
Race Finish March 16, 2024 8:09:06pm UTC
Outcome No win (3 of 5)
Opponents 1. adocys (85.57 wpm)
Accuracy 99.1%
Points 204.60
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 on e quantity is errelated to a change in another. How does the speed of a falling object change as a function of time? How deoes the level of water in a barrel change as a function of the amount of liquid poured into it? We see change occurring in nrearly everything we observe in the world and universe, and powerful modrern 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 preciesse developments of there se 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.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 327 1298 118 270 105 180 533 218 112 160 152 49 309 160 151 88 147 177 79 208 77 76 83 76 178
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 99 79 188 145 96 160 137 76 174 177 75 172 61 199 185 131 105 124 87 190 114 112 89 148 75
Character c h a n g e i n o n - e q u a n t i t y
Milliseconds 421 52 159 53 249 147 107 133 168 122 114 95 497 296 55 74 150 136 124 180 257 71 89 84 129
Character i s e r -r -e r e l a t e d t o a c h a n g
Milliseconds 223 376 165 175 223 186 159 112 145 315 80 175 148 160 89 151 93 91 249 185 303 92 87 96 112
Character e i n a n o t h e r . H o w d o e s t h
Milliseconds 132 92 162 162 173 187 89 153 122 137 125 90 205 100 259 208 158 106 120 114 83 115 124 164 100
Character e s p e e d o f a f a l l i n g o b j e
Milliseconds 109 167 193 164 120 153 182 92 160 89 104 167 117 361 150 302 155 432 197 190 117 131 173 216 97
Character c t c h a n g e a s a f u n c t i o n o
Milliseconds 132 215 128 159 104 93 107 100 136 121 120 191 120 124 101 180 80 184 87 205 45 184 114 164 128
Character f t i m e ? H o w d e -e o e s t h e l e
Milliseconds 97 60 201 91 144 156 311 209 267 248 103 138 107 176 418 208 58 158 127 139 97 76 103 168 89
Character v e l o f w a t e r i n a b a r r e l
Milliseconds 243 152 92 120 165 136 84 287 180 176 164 76 148 321 179 501 220 147 254 94 205 167 176 200 148
Character c h a n g e a s a f u n c t i o n o f t
Milliseconds 281 79 136 168 133 151 249 160 191 96 140 132 137 96 195 97 195 57 184 92 188 203 152 158 174
Character h e a m o u n t o f l i q u i d p o u r e
Milliseconds 72 94 86 130 122 190 84 227 127 89 181 104 83 160 104 155 132 164 126 131 417 203 175 104 160
Character d i n t o i t ? W e s e e c h a n g e
Milliseconds 185 119 152 168 169 109 132 834 104 310 167 371 332 110 227 244 164 169 236 58 92 109 98 131 110
Character o c c u r r i n g i n n r -r e a r l y e v e
Milliseconds 197 137 146 108 177 391 153 215 180 297 192 179 170 132 132 423 76 133 222 153 156 155 269 156 144
Character r y t h i n g w e o b s e r v e i n t h e
Milliseconds 51 99 165 69 147 68 100 102 124 98 108 384 161 135 184 136 239 145 128 140 169 141 220 72 96
Character w o r l d a n d u n i v e r s e , a n d
Milliseconds 75 144 104 116 104 88 159 116 89 143 160 222 187 151 101 139 91 170 163 120 112 176 36 200 72
Character p o w e r f u l m o d r -r e r n i n s t r u m
Milliseconds 208 68 64 64 88 225 67 180 152 132 132 104 196 361 103 120 160 1033 249 150 116 172 136 76 240
Character e n t s h e l p u s s e e m o r e a n d
Milliseconds 117 78 85 152 112 200 117 96 181 180 170 144 112 164 204 149 95 172 149 100 144 143 84 103 117
Character m o r e , -, . I n t h i s s e c t i o n
Milliseconds 97 187 145 95 152 200 413 223 88 253 292 104 195 52 152 139 109 124 156 170 208 70 165 231 125
Character w e i n t r o d u c e t h e i d e a s o f
Milliseconds 500 159 98 166 147 146 135 116 381 120 179 180 120 142 79 109 106 160 77 187 168 200 105 172 134
Character a v e r a g e a n d i n s t a n t a n e o u
Milliseconds 74 452 215 144 112 176 124 137 152 131 108 133 98 193 188 84 184 121 103 127 562 291 112 284 157
Character s r a t e s o f c h a n g e , a n d s h
Milliseconds 124 79 180 165 171 144 172 99 181 99 79 134 89 112 116 92 127 169 131 192 44 164 84 133 103
Character o w t h a t t h e y a r e c l o s e l y
Milliseconds 129 119 97 211 89 76 117 111 155 83 112 102 127 144 119 92 130 164 211 180 63 185 65 179 128
Character r e l a t e d t o t h e s l o p e o f a
Milliseconds 164 148 196 96 117 151 184 96 140 96 109 159 92 89 92 131 92 177 195 165 87 156 93 96 108
Character c u r v e a t a p o i n t P o n t h
Milliseconds 110 145 118 93 209 141 122 145 158 142 197 140 180 231 192 184 112 105 263 289 259 310 121 193 83
Character e c u r v e . W e g i v e p r e c i e s -s
Milliseconds 84 97 130 106 96 228 156 104 144 356 256 157 160 79 138 138 145 215 101 143 194 121 178 228 321
Character -e s e d e v e l o p m e n t s o f t h e r e
Milliseconds 119 67 141 98 141 197 160 132 128 175 172 221 91 100 72 145 115 153 103 99 122 91 83 82 127
Character - -e -r s e i m p o r t a n t c o n c e p t s
Milliseconds 111 387 151 119 260 184 125 163 200 176 188 89 199 146 50 132 83 173 69 83 132 160 140 127 173
Character i n t h e n e x t c h a p t e r , b u t
Milliseconds 68 308 80 145 163 88 104 64 159 92 317 222 121 221 76 100 304 119 145 63 169 120 131 181 92
Character f o r n o w w e u s e a n i n f o r m
Milliseconds 101 113 90 92 101 151 144 140 96 136 136 169 191 120 172 120 148 72 130 181 168 112 101 79 132
Character a l a p p r o a c h s o y o u w i l l s
Milliseconds 132 111 143 174 93 163 77 147 144 244 104 104 236 92 118 115 181 94 156 176 92 164 158 86 137
Character e e h o w t h e y l e a d n a t u r a l l
Milliseconds 223 149 115 430 154 127 66 152 74 94 87 101 180 70 153 68 160 180 93 156 100 131 497 135 148
Character y t o t h e m a i n i d e a o f t h i
Milliseconds 160 140 161 99 83 173 84 84 97 363 81 119 127 76 205 128 180 152 188 160 137 63 196 68 133
Character s c h a p t e r , t h e l i m i t . T h e
Milliseconds 159 96 196 69 125 118 135 125 68 139 112 177 84 176 160 192 165 175 136 108 140 110 262 212 137
Character i d e a o f a l i m i t p l a y s a
Milliseconds 96 155 92 170 139 264 167 108 87 131 118 216 105 195 152 140 121 175 242 122 184 473 191 245 108
Character f o u n d a t i o n a l r o l e t h r o u g h
Milliseconds 163 84 64 201 68 135 150 82 136 36 149 94 125 170 111 171 690 154 244 62 126 8 66 122 65
Character o u t c a l c u l u s .
Milliseconds 203 72 123 97 216 158 94 180 95 181 318 227 110
WPM Timing
Seconds WPM
2.74 26.31
5.47 57.01
8.21 67.24
10.95 67.97
13.68 66.66
16.42 66.51
19.15 68.91
21.89 71.81
24.63 70.17
27.36 72.36
30.1 72.56
32.84 72.72
35.57 71.52
38.31 71.42
41.05 72.8
43.78 72.91
46.52 71.71
49.25 71.87
51.99 70.63
54.73 71.48
57.46 71.84
60.2 72.76
62.94 72.45
65.67 72.18
68.41 72.62
71.14 72.19
73.88 72.12
76.62 72.36
79.35 72.59
82.09 72.21
84.83 73.14
87.56 73.73
90.3 74.29
93.04 74.42
95.77 74.43
98.51 74.06
101.24 74.08
103.98 73.51
106.72 73.99
109.45 74.11
112.19 74.55
114.93 74.87
117.66 75.06
120.4 75.15
123.14 75.43
125.87 75.7
128.61 75.77
131.34 75.65
134.08 75.54
136.82 75.78