The (amirgambit)

Race #1384

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Official speed 92.07 wpm (112.61 seconds elapsed during race)
Without ending ping 92.27 wpm (248 ms delay sending score to TypeRacer’s server)
Timerless 92.57 wpm (356 ms elapsed before first character typed; 112.01 seconds elapsed during race)
Timerless minus one 92.46 wpm, ignoring the first character typed
Race Start September 13, 2023 3:14:49am UTC
Race Finish September 13, 2023 3:16:41am UTC
Outcome Win (1 of 5)
Opponents 3. luimbakiml (66.78 wpm)
4. tahashemy (65.64 wpm)
Accuracy 97.6%
Points 248.60
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 one quantity is realated to a change in another. How does the speed of a falling object change as a funcrtionfunction of time? How does the level of water in a barrel changes as a function of teh athe amount of liquid puououred into it? We see hchange occurring in nearly everything we observe int he in the world and universe, and powerful modern instruments help us see more and more. I nn this section we introduce the ideas of eveaverage and instanteaneous reate rates of change, and show that they are closely related to the slope of a curve at a opinpoint P on the curve. We give precise developments of thseseese imporatntant concepts in the next chapter, but for now we use an informal approach so you will see how tehy they lead naturally to the main idea of this chapter, the limit. The idea of a mlimit plays a foundational role throughout calcullus.us.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 356 178 107 143 113 87 180 115 106 42 98 114 132 109 128 72 152 169 69 57 99 71 54 60 95
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 98 57 139 97 72 92 74 142 111 195 27 184 41 168 71 84 99 96 83 96 29 84 86 83 156
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 84 82 113 107 158 70 114 82 97 114 403 73 26 154 141 98 126 55 183 11 269 84 153 112 86
Character r e a -a l a t e d t o a c h a n g e i n
Milliseconds 98 111 64 63 432 224 56 40 71 153 25 143 57 111 26 182 365 85 83 113 110 71 141 84 84
Character a n o t h e r . H o w d o e s t h e s p
Milliseconds 68 45 110 72 26 156 52 72 70 127 193 151 84 72 97 103 112 43 69 138 98 102 108 98 85
Character e e d o f a f a l l i n g o b j e c t c
Milliseconds 111 125 156 29 95 113 59 123 127 223 154 194 140 69 72 58 69 83 113 84 98 168 141 10 198
Character h a n g e a s a f u n c r t i o n -f -u -n -c -r
Milliseconds 109 115 195 71 85 208 127 110 58 266 152 110 87 167 58 196 0 14 208 45 361 0 0 0 0
Character -t -i -o -n f u n c t i o n o f t i m e ? H o w
Milliseconds 0 0 0 0 407 29 166 84 155 36 43 102 55 99 110 71 224 28 56 56 264 253 266 226 82
Character d o e s t h e l e v e l o f w a t e r
Milliseconds 27 140 54 129 28 56 112 56 84 29 96 84 127 57 82 113 126 71 98 126 55 56 108 87 44
Character i n a b a r r e l c h a n g e s -s a s a
Milliseconds 83 82 114 24 199 98 168 82 183 43 83 111 142 71 81 99 97 69 71 393 139 43 110 84 98
Character f u n c t i o n o f t e h a -a -t -e -h - t h
Milliseconds 99 85 97 184 69 210 30 55 69 125 70 126 84 125 100 0 208 40 436 98 0 0 0 224 11
Character e a m o u n t o f l i q u i d p u o u -u -o
Milliseconds 144 41 167 128 69 124 183 126 56 97 224 85 168 183 166 72 83 155 110 142 180 57 126 322 126
Character -u o u r e d i n t o i t ? W e s e e h -h
Milliseconds 110 184 41 97 38 171 57 55 99 141 82 99 84 139 253 84 210 196 69 113 97 139 113 225 321
Character c h a n g e o c c u r r i n g i n n e a r l
Milliseconds 80 101 56 113 13 84 112 211 70 154 98 112 180 140 72 98 138 153 100 69 127 82 59 57 83
Character y e v e r y t h i n g w e o b s e r v e i
Milliseconds 93 86 171 124 83 88 83 139 71 83 111 86 55 140 56 83 111 97 183 41 72 181 54 44 73
Character n t h e -h -e - -i -n -t - i n t h e w o r l d
Milliseconds 81 113 0 180 14 109 297 0 0 126 0 0 0 225 98 98 125 53 115 58 123 14 224 16 282
Character a n d u n i v e r s e , a n d p o w e r f
Milliseconds 55 124 71 267 68 153 155 40 115 83 98 87 276 98 127 176 75 126 70 238 389 71 30 54 294
Character u l m o d e r n i n s t r u m e n t s h e l
Milliseconds 88 83 150 240 56 85 167 85 111 125 182 83 44 166 142 83 195 84 84 57 96 83 102 123 73
Character p u s s e e m o r e a n d m o r e . I
Milliseconds 110 112 112 114 65 117 125 182 126 25 74 76 75 99 71 112 70 154 56 82 42 57 223 71 196
Character n -n - n t h i s s e c t i o n w e i n t
Milliseconds 167 194 287 106 251 71 83 70 58 96 89 107 84 196 196 60 63 89 124 98 70 141 80 89 125
Character r o d u c e t h e i d e a s o f e v e -e -v
Milliseconds 154 140 154 141 55 209 57 124 73 53 127 55 44 180 70 262 157 56 140 85 98 154 98 252 137
Character -e a v e r a g e a n d i n s t a n t e -e a n e
Milliseconds 127 13 72 126 85 84 112 54 85 111 128 97 98 125 128 71 320 279 391 98 405 266 84 111 58
Character o u s r e a t e -r -e -a -t -e - r a t e s o f
Milliseconds 265 83 99 154 253 71 26 99 43 95 310 0 0 0 0 0 252 83 99 26 182 183 55 98 71
Character c h a n g e , a n d s h o w t h a t t h e
Milliseconds 224 69 98 84 110 71 98 140 71 111 85 83 96 72 56 57 70 111 181 13 269 168 83 113 40
Character y a r e c l o s e l y r e l a t e d t o
Milliseconds 171 51 100 58 42 110 184 54 185 26 69 113 112 55 294 392 97 72 82 56 167 16 194 71 168
Character t h e s l o p e o f a c u r v e a t a
Milliseconds 72 95 34 162 212 249 255 70 113 10 241 111 44 162 47 224 78 84 187 24 72 140 128 96 118
Character o p i n -o -p -i -n p o i n t P o n t h e c
Milliseconds 232 168 14 126 112 351 0 0 0 252 41 125 86 83 168 167 184 98 69 110 113 84 28 127 111
Character u r v e . W e g i v e p r e c i s e d e v
Milliseconds 113 84 208 28 83 127 237 168 133 78 166 13 86 141 155 126 41 209 71 126 209 170 125 168 54
Character e l o p m e n t s o f t h s e -e -s s e -e -s e s
Milliseconds 112 59 209 56 168 153 56 112 55 71 72 108 71 99 138 168 140 252 112 85 0 442 188 225 152
Character e i m p o r a t n -n -t -a t a n t c o n c e p t
Milliseconds 56 99 367 81 141 69 124 223 87 24 435 168 153 99 55 85 99 99 167 68 59 139 209 27 97
Character s i n t h e n e x t c h a p t e r , b u
Milliseconds 86 82 73 111 112 15 208 14 210 57 111 197 73 82 153 83 127 140 238 56 95 73 97 167 56
Character t f o r n o w w e u s e a n i n f o r
Milliseconds 139 44 166 29 151 13 73 83 55 128 210 84 70 141 98 56 70 112 99 97 140 93 61 153 56
Character m a l a p p r o a c h s o y o u w i l l
Milliseconds 97 113 84 112 69 113 140 83 141 98 194 128 111 112 41 140 83 84 99 28 127 68 197 125 71
Character s e e h o w t e h y -t -e -h -y - t h e y l e
Milliseconds 154 83 210 69 72 71 71 154 208 73 0 193 70 337 0 0 0 0 319 57 182 181 113 98 152
Character a d n a t u r a l l y t o t h e m a i n
Milliseconds 128 110 84 44 124 127 140 64 131 128 140 98 54 182 56 100 41 98 100 97 25 127 56 113 154
Character i d e a o f t h i s c h a p t e r , t h e
Milliseconds 70 98 153 99 124 70 141 84 112 55 44 83 125 97 74 220 100 83 98 99 70 82 99 65 116
Character l i m i t . T h e i d e a o f a m -m l
Milliseconds 71 112 84 139 72 111 190 92 152 197 83 168 126 110 170 69 100 82 156 67 113 208 156 473 185
Character i m i t p l a y s a f o u n d a t i o n a l
Milliseconds 53 100 127 66 114 128 125 126 69 198 92 89 154 153 58 55 152 45 70 152 26 87 85 109 124
Character r o l e t h r o u g h o u t c a l c u l l u
Milliseconds 183 100 70 195 112 99 138 195 16 222 278 296 534 180 86 130 93 210 85 0 432 97 114 167 28
Character s . -. -s -u -l u s .
Milliseconds 111 99 265 126 111 409 166 69 98
WPM Timing
Seconds WPM
2.25 90.58
4.5 106.56
6.76 106.56
9.01 103.9
11.26 102.3
13.51 106.56
15.77 107.32
18.02 105.9
20.27 98.27
22.52 99.1
24.77 102.2
27.03 101.68
29.28 98.78
31.53 98.57
33.78 96.62
36.04 94.91
38.29 95.91
40.54 97.68
42.79 96.19
45.04 95.91
47.3 95.4
49.55 96.15
51.8 97.3
54.05 95.91
56.3 96.55
58.56 95.7
60.81 94.92
63.06 92.86
65.31 93.33
67.57 94.13
69.82 94.36
72.07 94.07
74.32 93.32
76.57 93.56
78.83 93.77
81.08 93.09
83.33 91.87
85.58 91.7
87.84 92.08
90.09 92.84
92.34 93.44
94.59 92.99
96.84 92.81
99.1 93.36
101.35 94.13
103.6 94.05
105.85 93.64
108.11 94.02
110.36 93.3
112.61 92.07