Micha (derpeus)

Race #5167

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Official speed 84.07 wpm (123.33 seconds elapsed during race)
Without ending ping 84.23 wpm (237 ms delay sending score to TypeRacer’s server)
Timerless 84.47 wpm (345 ms elapsed before first character typed; 122.74 seconds elapsed during race)
Timerless minus one 84.37 wpm, ignoring the first character typed
Race Start November 2, 2023 4:37:40pm UTC
Race Finish November 2, 2023 4:39:44pm UTC
Outcome No win (2 of 5)
Opponents 1. racen55 (104.90 wpm)
3. raket124 (80.55 wpm)
4. darus (78.23 wpm)
Accuracy 97.3%
Points 226.99
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 one quantity is related to a change in another. How does the speed of a falling object changes as a function of time? How doest t ts s the leve l of water in a barrele change as afun fyuunction of the amount of liquid opoured into it? We see cahgnehange occuring ring in nearly everything we obse verver in in thge e world and universe, and powerful modern instruments help us see more and more. In this section we introduce the idead s of averatgge and instantaneous rates of change, and show that they are closely related to the slope of a curve at a poinrt t P on the curve. WE e give precise developments of these importants concepts in the next chapter, but for now we use an informal approacy h so you wikl l,lll see how they lead naturally to the main idea of this chapter, the mlimit. The idea of a limit plays a foundational role throughtout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 345 181 199 166 353 150 278 152 131 137 100 104 164 97 296 107 154 151 113 155 125 41 79 57 94
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 111 159 177 134 120 141 428 119 206 170 35 172 58 157 88 85 85 112 37 94 62 42 97 217 168
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 154 96 105 109 105 37 91 150 27 101 108 87 104 73 263 73 208 134 157 99 196 182 187 157 93
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 70 165 73 100 158 87 113 193 79 146 90 38 114 104 185 71 122 44 79 79 91 89 55 101 78
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 100 150 123 134 53 83 194 94 305 153 40 131 143 87 98 61 161 205 167 34 77 110 96 122 131
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 134 63 90 142 252 116 138 248 91 64 156 133 33 112 80 165 381 244 227 185 158 83 218 103 97
Character n g e s - -s a s a f u n c t i o n o f
Milliseconds 167 56 54 126 14 349 115 102 77 113 89 125 144 290 243 185 58 224 24 25 31 124 156 39 68
Character t i m e ? H o w d o e s t t -t - -t -s t -t s
Milliseconds 173 73 30 98 202 134 143 168 25 107 167 94 91 51 120 66 164 276 97 116 113 54 89 302 169
Character - -s - s t h e l e v e - l o f w a t e
Milliseconds 95 176 116 115 153 113 139 100 96 73 152 119 104 59 82 349 253 47 475 60 54 230 93 79 114
Character r i n a b a r r e l e -e c h a n g e a s
Milliseconds 58 82 172 79 44 77 169 137 152 104 139 57 86 111 316 126 171 111 124 132 40 54 98 249 107
Character a f u n -n -u -f f y u -u -y u n c t i o n o f
Milliseconds 103 93 385 161 153 204 132 113 126 119 114 0 374 129 152 202 90 209 40 41 35 137 140 59 71
Character t h e a m o u n t o f l i q u i d o -o p o
Milliseconds 213 44 79 58 126 158 85 130 161 194 123 271 149 49 125 91 208 106 74 225 112 213 340 266 229
Character u r e d i n t o i t ? W e s e e c a h g
Milliseconds 171 336 126 184 95 58 45 85 131 82 164 73 235 168 532 220 100 182 128 147 33 293 128 35 203
Character n e -e -n -g -h -a h a n g e o c c u r i n g - -g -n
Milliseconds 10 18 195 131 99 131 146 236 57 142 146 71 82 189 152 147 68 123 75 87 94 89 226 113 132
Character -i r i n g i n n e a r l y e v e r y t h i n
Milliseconds 99 167 109 79 72 78 132 45 119 218 18 110 46 90 186 65 182 111 110 97 49 173 100 55 105
Character g w e o b s e - v e -e -v r v e r i n -n -i -
Milliseconds 78 38 123 98 107 197 141 99 268 238 348 156 86 250 131 109 163 90 142 58 88 71 295 131 99
Character -r i n t h g e - -e -g e w o r l d a n d
Milliseconds 114 126 140 46 125 132 68 24 71 74 259 132 110 154 99 91 113 115 77 87 113 167 91 80 71
Character u n i v e r s e , a n d p o w e r f u l m o
Milliseconds 156 161 84 87 110 133 95 94 103 101 111 49 119 48 164 75 115 63 57 200 54 84 105 144 93
Character d e r n i n s t r u m e n t s h e l p u s
Milliseconds 77 210 90 87 126 116 53 79 113 154 75 177 77 95 118 60 117 130 94 141 145 116 214 58 128
Character s e e m o r e a n d m o r e . I n t h i
Milliseconds 259 54 335 167 216 68 57 65 75 176 75 112 137 79 68 81 75 119 86 222 160 43 156 69 36
Character s s e c t i o n w e i n t r o d u c e t h
Milliseconds 80 53 175 78 212 174 58 8 71 101 115 80 124 213 63 87 187 60 486 87 112 207 99 131 76
Character e i d e a d - -d s o f a v e r a t g -g -t g
Milliseconds 80 73 180 14 166 110 171 211 276 114 105 103 165 108 153 159 117 158 172 110 95 159 206 115 96
Character e a n d i n s t a n t a n e o u s r a t e s
Milliseconds 62 108 167 92 78 55 140 53 73 86 86 68 149 245 252 126 246 58 125 80 147 92 162 67 189
Character o f c h a n g e , a n d s h o w t h a t
Milliseconds 79 165 42 80 194 104 123 76 112 29 121 126 85 101 53 48 141 25 62 108 56 124 67 105 34
Character t h e y a r e c l o s e l y r e l a t e d
Milliseconds 86 114 49 123 41 66 126 78 82 32 178 72 135 30 94 142 194 50 147 89 77 425 105 130 213
Character t o t h e s l o p e o f a c u r v e
Milliseconds 100 180 90 114 132 100 44 77 93 97 154 74 63 121 165 92 55 125 105 145 150 107 184 86 74
Character a t a p o i n r t - -t -r t P o n t h e
Milliseconds 141 203 187 241 96 180 57 132 144 192 0 64 350 147 82 152 47 157 189 213 95 84 140 68 79
Character c u r v e . W E - -E e g i v e p r e c i
Milliseconds 42 283 109 77 200 68 120 101 385 106 204 220 114 133 34 425 145 45 68 54 173 147 108 211 92
Character s e d e v e l o p m e n t s o f t h e s e
Milliseconds 282 195 130 265 177 137 84 68 187 40 277 101 94 126 60 71 148 92 71 140 52 54 143 186 114
Character i m p o r t a n t s - -s c o n c e p t s i n
Milliseconds 344 79 69 196 98 156 76 85 77 117 178 234 130 34 148 25 73 202 240 94 90 83 71 74 55
Character t h e n e x t c h a p t e r , b u t f o
Milliseconds 98 151 59 97 57 171 31 213 142 66 169 104 9 225 147 91 189 152 61 153 125 98 49 200 87
Character r n o w w e u s e a n i n f o r m a l
Milliseconds 98 82 80 42 76 114 180 74 122 165 61 61 67 158 126 125 131 70 58 101 98 105 94 116 128
Character a p p r o a c y - -y h s o y o u w i k l
Milliseconds 167 120 140 130 107 166 200 118 97 269 132 233 30 94 79 114 156 74 25 72 99 64 196 0 96
Character l -l - -l -k , l -l -, l l s e e h o w t h e y
Milliseconds 52 247 114 114 116 205 128 290 131 219 130 64 77 78 188 255 51 56 139 311 155 94 79 115 74
Character l e a d n a t u r a l l y t o t h e m a i
Milliseconds 142 45 94 106 70 138 104 95 114 91 110 147 311 260 65 246 57 90 196 44 95 59 127 46 130
Character n i d e a o f t h i s c h a p t e r , t
Milliseconds 53 61 254 93 186 76 136 247 150 30 155 51 39 77 70 170 104 48 170 147 91 97 122 99 141
Character h e m -m l i m i t . T h e i d e a o f a
Milliseconds 68 78 58 130 309 203 86 104 127 114 291 119 426 208 54 106 197 117 146 76 160 116 158 186 101
Character l i m i t p l a y s a f o u n d a t i o n
Milliseconds 308 135 110 79 102 81 137 182 135 92 101 118 137 69 120 233 71 55 204 19 118 111 82 23 82
Character a l r o l e t h r o u g h t -t o u t c a l c
Milliseconds 175 149 97 180 72 159 55 73 157 100 136 110 73 45 147 38 513 233 89 42 56 302 70 81 126
Character u l u s .
Milliseconds 159 183 309 101 166
WPM Timing
Seconds WPM
2.47 63.25
4.93 75.41
7.4 82.71
9.87 87.57
12.33 91.47
14.8 94.06
17.27 93.83
19.73 91.22
22.2 89.74
24.67 89.52
27.13 84.48
29.6 84.33
32.06 84.2
34.53 80.28
37 81.73
39.46 80.28
41.93 79.85
44.4 77.84
46.86 77.07
49.33 79.06
51.8 77.15
54.26 75.63
56.73 77.21
59.2 78.65
61.66 79.01
64.13 80.46
66.6 80.91
69.06 80.62
71.53 80.69
74 81.09
76.46 83.02
78.93 83.16
81.4 84.03
83.86 83.14
86.33 82.85
88.79 82.57
91.26 82.97
93.73 82.71
96.19 83.33
98.66 84.17
101.13 84.37
103.59 83.63
106.06 83.05
108.53 83.26
110.99 84.01
113.46 84.08
115.93 83.85
118.39 84.03
120.86 84.49
123.33 84.07