Billy Madison (billymadison69)

Race #902

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Official speed 74.28 wpm (139.58 seconds elapsed during race)
Without ending ping 74.40 wpm (229 ms delay sending score to TypeRacer’s server)
Timerless 75.15 wpm (1,383 ms elapsed before first character typed; 137.97 seconds elapsed during race)
Timerless minus one 75.06 wpm, ignoring the first character typed
Race Start March 16, 2025 9:45:51pm UTC
Race Finish March 16, 2025 9:48:11pm UTC
Outcome No win (4 of 4)
Opponents 2. zoat (84.97 wpm)
Accuracy 96.8%
Points 200.54
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 hels ps uus undessrstand how a change in one quantity is reallated to a change in another. How sdoes the speped of a falling objetct change as a function of time? How sodoes the level of water in a barrel change ass a a fucntino nctionof thefunction of the amount of liquid poured into it? We see change occurring in nearyly everything we obseve rve in teh worlhe world and universe, and powerful modern instruments help us see more and more. In this sectin weoon wen we introduce the ideas of average and instantaneous rates of change, and show that thyeey are closely related oto teh slhe slope of a curve at a point P on the curve. We give precise developments of these important concepts in the enxt next chapetter, but for now we use an informal approach so you will see how they lead nnaturllyally to themain main indea of this chapter, the limit. The idea oa f a limit play a s 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 1383 219 164 278 58 253 166 134 45 166 70 66 49 123 146 80 139 150 80 108 100 23 82 56 130
Character e l s - -s p s u u -u s u n d e s s -s -s r s t
Milliseconds 116 67 281 54 292 111 211 164 97 125 411 294 129 80 120 159 55 180 251 26 419 161 177 178 135
Character a n d h o w a c h a n g e i n o n e q
Milliseconds 177 169 62 69 169 80 111 59 153 28 194 84 83 70 132 103 12 135 94 55 146 94 127 73 197
Character u a n t i t y i s r e a l -l -a l a t e d t o
Milliseconds 81 125 81 299 109 107 111 50 187 85 64 145 56 569 166 198 103 205 58 103 80 188 78 119 52
Character a c h a n g e i n a n o t h e r . H o w
Milliseconds 115 180 160 176 85 72 90 88 96 52 264 117 32 149 67 103 102 83 100 55 127 32 300 171 148
Character s -s d o e s t h e s p e p -p e d o f a
Milliseconds 69 135 324 110 121 58 130 87 128 53 67 80 100 84 156 0 443 248 200 191 234 90 104 79 59
Character f a l l i n g o b j e t -t c t c h a n g e a
Milliseconds 156 106 36 138 107 105 52 104 116 150 184 49 326 325 226 226 83 124 92 75 104 140 106 204 119
Character s a f u n c t i o n o f t i m e ? H o w
Milliseconds 545 89 112 66 186 145 138 64 236 56 22 57 59 253 72 52 322 83 191 9 254 171 311 195 112
Character s o -o -s d o e s t h e l e v e l o f w a
Milliseconds 116 148 108 292 145 133 107 92 73 117 100 61 35 84 266 26 161 64 118 0 185 104 31 182 113
Character t e r i n a b a r r e l c h a n g e a s
Milliseconds 157 163 69 67 146 82 88 83 79 146 38 269 116 63 135 53 193 111 110 84 54 97 98 192 125
Character s a - -a - -s a f u c n t i n o - -o -n -i -t
Milliseconds 0 97 141 42 376 110 116 218 236 210 105 397 128 125 56 212 30 121 28 0 306 115 119 69 135
Character -n -c n c t i o n o f t h e -t -h -e -f -u -n -c -t -i -o -n
Milliseconds 210 116 265 104 221 27 121 44 216 81 67 123 50 28 549 0 0 119 0 0 0 0 0 0 0
Character -o -f - f u n c t i o n o f t h e a m o u n t
Milliseconds 0 0 0 719 53 162 116 245 37 38 108 78 289 108 80 173 64 30 57 239 71 154 60 216 105
Character o f l i q u i d p o u r e d i n t o i t
Milliseconds 62 181 68 52 132 70 238 117 180 612 107 331 220 1286 141 123 196 30 171 87 161 30 68 187 61
Character ? W e s e e c h a n g e o c c u r r i n g
Milliseconds 232 60 294 387 104 89 197 130 44 151 81 54 148 55 64 60 149 54 147 115 120 162 110 82 106
Character i n n e a r y -y l y e v e r y t h i n g w
Milliseconds 75 315 99 118 154 79 115 108 266 300 209 185 82 65 137 142 82 86 125 66 133 66 90 160 0
Character e o b s e v e - -e -v r v e i n t e h w o
Milliseconds 64 134 135 166 87 106 382 184 123 267 107 120 183 204 71 107 150 75 49 105 131 0 118 337 79
Character r l -l -r -o -w - -h -e h e w o r l d a n d u n i
Milliseconds 116 82 327 131 131 282 145 138 606 241 103 54 110 84 99 118 79 78 84 94 83 48 118 175 59
Character v e r s e , a n d p o w e r f u l m o d e r
Milliseconds 136 183 62 132 107 125 50 72 139 104 27 189 161 130 101 69 251 127 165 87 170 146 69 163 66
Character n i n s t r u m e n t s h e l p u s s e e
Milliseconds 105 35 141 120 57 116 151 79 187 97 36 81 107 107 148 105 77 151 131 448 105 69 128 195 121
Character m o r e a n d m o r e . I n t h i s s
Milliseconds 85 139 149 79 65 69 103 114 49 51 133 165 85 67 117 64 240 106 42 136 79 50 67 49 132
Character e c t i n w e -e -w - -n o o n w e -e -w - -n -o n
Milliseconds 56 228 453 72 108 72 133 115 218 122 95 96 212 19 50 134 71 101 302 98 215 303 163 216 110
Character w e i n t r o d u c e t h e i d e a s o f
Milliseconds 146 83 95 163 44 127 176 52 170 119 115 81 101 160 89 18 108 216 94 152 125 115 145 190 204
Character a v e r a g e a n d i n s t a n t a n e o u
Milliseconds 123 278 221 222 90 132 67 84 148 244 99 97 77 252 53 160 92 128 135 123 190 138 361 141 147
Character s r a t e s o f c h a n g e , a n d s h
Milliseconds 210 163 215 100 137 58 67 118 209 24 106 253 150 90 132 100 98 134 68 82 164 52 85 307 99
Character o w t h a t t h y e -e -y e y a r e c l o s
Milliseconds 132 112 53 210 56 138 35 59 159 495 222 254 262 116 140 77 89 67 69 104 84 350 79 144 87
Character e l y r e l a t e d o -o t o t e h s l -l -s
Milliseconds 109 49 276 135 47 100 170 81 104 65 162 100 184 362 162 95 32 66 149 0 50 136 132 255 116
Character - -h -e h e s l o p e o f a c u r v e a t
Milliseconds 207 124 84 300 120 87 145 77 158 162 170 80 187 100 67 86 58 191 201 106 174 53 127 267 252
Character a p o i n t P o n t h e c u r v e .
Milliseconds 128 137 66 185 862 201 169 140 93 185 167 123 47 113 114 105 75 87 120 107 127 147 91 102 74
Character W e g i v e p r e c i s e d e v e l o p m e
Milliseconds 258 178 104 411 148 83 55 101 163 87 412 231 220 64 117 86 250 170 133 115 30 186 114 259 42
Character n t s o f t h e s e i m p o r t a n t c o
Milliseconds 125 76 232 149 192 73 76 268 58 91 127 77 110 114 164 133 220 0 196 134 171 83 97 188 23
Character n c e p t s i n t h e e n x t - -t -x -n -e n
Milliseconds 74 239 46 243 122 96 48 123 96 65 73 110 51 20 218 30 168 193 74 191 98 122 192 125 220
Character e x t c h a p e t -t -e t e r , b u t f o r
Milliseconds 0 162 206 33 167 66 91 75 164 136 281 97 105 149 70 56 97 165 152 89 126 170 128 145 43
Character n o w w e u s e a n i n f o r m a l a p
Milliseconds 142 70 99 174 295 139 107 134 54 120 61 153 96 61 166 91 132 85 88 34 118 116 98 147 208
Character p r o a c h s o y o u w i l l s e e h o
Milliseconds 336 181 74 92 186 130 108 132 50 82 135 149 71 61 86 117 163 123 52 129 202 135 46 175 38
Character w t h e y l e a d n n -n a t u r l l y -y -l -l
Milliseconds 173 116 114 101 101 50 65 224 0 168 209 82 206 209 288 196 197 139 116 260 124 238 223 125 199
Character a l l y t o t h e m a i n - -n -i -a -m m a i
Milliseconds 244 108 117 196 48 163 68 67 102 101 30 206 157 39 100 52 235 89 127 109 184 209 161 171 46
Character n i n -n d e a o f t h i s c h a p t e r ,
Milliseconds 87 69 140 45 391 350 149 118 117 172 99 79 130 87 36 83 67 155 141 214 149 162 157 71 72
Character t h e l i m i t . T h e i d e a o a -
Milliseconds 61 210 91 65 20 300 136 171 150 59 144 55 241 110 99 0 308 57 161 111 130 133 133 55 362
Character -a f a l i m i t p l a y a - -a - s a
Milliseconds 268 165 88 96 30 175 93 168 140 99 45 139 172 108 80 81 68 65 492 112 222 227 89 113 79
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 121 65 87 243 35 125 126 84 32 101 229 88 82 389 61 188 84 61 173 94 119 18 79 234 81
Character o u t c a l c u l u s .
Milliseconds 192 60 144 88 354 94 153 234 67 281 175 61 153
WPM Timing
Seconds WPM
2.79 38.69
5.58 62.33
8.37 54.45
11.17 68.78
13.96 67.06
16.75 74.51
19.54 76.15
22.33 77.37
25.12 74.99
27.92 76.09
30.71 76.98
33.5 79.88
36.29 75.72
39.08 70.31
41.87 69.06
44.67 70.12
47.46 68.52
50.25 70.21
53.04 70.14
55.83 70.93
58.62 69.19
61.42 69.17
64.21 70.46
67 71.64
69.79 73.42
72.58 71.75
75.37 71.64
78.16 72.16
80.96 72.19
83.75 73.08
86.54 72.8
89.33 73.08
92.12 72.29
94.91 72.57
97.71 72.71
100.5 72.72
103.29 73.19
106.08 73.87
108.87 73.52
111.66 73.61
114.46 74.12
117.25 74.82
120.04 74.78
122.83 74.15
125.62 73.46
128.41 74.1
131.21 73.9
134 73.61
136.79 74.22
139.58 74.28