Benjamin (benjaminsanta)

Race #11866

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Official speed 85.85 wpm (120.77 seconds elapsed during race)
Without ending ping 86.10 wpm (347 ms delay sending score to TypeRacer’s server)
Timerless 86.60 wpm (705 ms elapsed before first character typed; 119.72 seconds elapsed during race)
Timerless minus one 86.50 wpm, ignoring the first character typed
Race Start December 6, 2023 7:14:59am UTC
Race Finish December 6, 2023 7:16:59am UTC
Outcome Win (1 of 5)
Accuracy 94.4%
Points 231.79
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 Calcluulius is a tool that helps us uimndenderstand how a changei n in one qualitynkitity is related to ca change in another. How does the speed o f a allfalling object change as a functioonn of time? Hpow pow does hte the l;evevel; of water in a brarrel change as a function of the moamouint nt of liquid porured into it? wEWe see cahgnchange occuring irin g in nearly everythiungng we observe in the world and uininiverse, and powerfcduul modern instirumebnnts help us see more and more. IUn n this sceection we introudduce the ideas of average and instanteaneous rates of chagnnge, and hsow show that they are closleely related to the slope of a curve at a point P on the cuvrve. We give precivse developments of these imporrtatant concetppts in the next hcchapter, but for now ewe use an informal approach so youl wi i will see how they lead natruaurally to the main moiidea o df this chapter, the mlimit. The idea odf af a limpliy plt plays a funoundational role throughout calculus.
Timing
Character C a l c l u -u -l u l i -i u s i s a t o o l
Milliseconds 705 84 71 194 54 172 271 134 13 159 61 320 184 95 81 73 76 77 78 113 0 59 131 164 60
Character t h a t h e l p s u s u i m n d e -e -d -n -m -i
Milliseconds 68 91 13 100 45 209 32 130 158 70 53 76 332 0 405 41 37 11 2 63 225 159 178 153 169
Character n d e r s t a n d h o w a c h a n g e i n
Milliseconds 85 45 74 112 95 119 52 275 104 58 102 127 25 79 108 86 53 72 66 100 24 73 79 15 72
Character - -n - -i i n o n e q u a l i t y -y -t -i -l n
Milliseconds 73 269 140 261 160 77 70 79 71 280 107 35 59 111 94 106 63 50 99 49 182 165 134 162 65
Character k i -i -k t i t y i s r e l a t e d t o c -c
Milliseconds 45 15 279 174 123 117 57 86 127 176 41 96 220 79 96 142 79 77 113 58 104 36 84 88 270
Character a c h a n g e i n a n o t h e r . H o w
Milliseconds 104 94 89 80 35 143 31 61 101 54 35 105 47 86 137 94 51 163 50 136 106 126 93 74 41
Character d o e s t h e s p e e d o - f a a l l
Milliseconds 87 81 63 61 90 54 78 59 76 95 52 127 133 94 88 87 123 297 83 61 106 89 102 77 130
Character -l -l -a f a l l i n g o b j e c t c h a n g e
Milliseconds 187 166 145 71 102 15 127 155 63 48 56 82 129 77 107 41 193 74 120 63 80 91 48 48 76
Character a s a f u n c t i o o n -n -o n o f t i m e
Milliseconds 106 52 107 74 114 29 63 89 76 156 48 120 131 77 255 141 38 87 126 108 91 75 44 73 49
Character ? H p o w - -w -o -p p -p o w d o e s h t e
Milliseconds 336 146 155 188 5 21 129 126 175 150 131 37 320 458 31 67 58 101 67 56 107 254 0 89 81
Character -h -t -e - t h e l ; e v -v -e -; e v e l ; - -; o
Milliseconds 287 0 0 0 204 45 89 79 298 3 22 129 203 169 146 41 95 78 99 12 72 335 141 92 117
Character f w a t e r i n a b r -r a r r e l c h a
Milliseconds 79 43 67 52 112 96 85 49 44 41 111 221 87 224 92 329 66 91 135 115 127 77 158 96 54
Character n g e a s a f u n c t i o n o f t h e
Milliseconds 121 7 68 94 97 91 96 63 117 59 71 58 103 149 59 159 52 82 104 91 34 122 73 81 81
Character m o -o -m a m o u i n t - -t -n -i n t o f l i q
Milliseconds 73 70 276 144 89 65 118 188 2 50 59 63 180 176 157 155 72 49 57 74 61 90 22 115 64
Character u i d p o r -r u r e d i n t o i t ? w E -E
Milliseconds 193 175 130 120 243 163 105 338 109 101 563 69 95 53 42 101 59 87 110 97 182 106 102 174 170
Character -w W e s e e c a h g n -c -a -h -g -n c h a n g e
Milliseconds 166 164 96 60 111 82 135 62 159 80 10 171 20 274 0 0 0 0 305 86 59 115 71 71 86
Character o c c u r i n g i -i - -g -n -i r i n - g i n
Milliseconds 158 68 149 94 117 98 71 77 67 49 238 160 149 149 158 63 80 65 76 385 152 121 91 50 65
Character n e a r l y e v e r y t h i u n g -g -n -u n g w
Milliseconds 197 60 21 52 128 69 79 125 112 111 64 171 141 57 11 5 144 22 210 150 244 39 120 52 106
Character e o b s e r v e i n t h e w o r l d a n
Milliseconds 94 74 87 156 83 168 60 181 44 82 59 55 60 107 35 102 110 77 113 72 94 82 65 54 99
Character d u i n i -i -n -i n i v e r s e , a n d p o w
Milliseconds 61 46 76 14 68 159 184 183 141 46 60 62 72 136 157 71 77 142 99 86 76 57 136 162 46
Character e r f c d u -u -d -c u l m o d e r n i n s t i -i
Milliseconds 141 48 189 7 15 25 273 168 143 14 139 123 328 75 63 116 95 99 91 139 81 85 98 64 300
Character r u m e b n -n -b n t s h e l p u s s e e m
Milliseconds 104 64 139 148 62 10 373 147 126 63 79 92 77 96 89 221 179 138 87 74 278 82 158 81 50
Character o r e a n d m o r e . I U n - -n -U n t h
Milliseconds 84 52 55 64 84 43 113 49 73 19 81 67 126 101 171 4 90 39 221 149 139 52 79 111 24
Character i s s c e -e -c e c t i o n w e i n t r o u d
Milliseconds 51 79 55 182 269 8 390 130 28 86 179 21 126 85 1004 286 59 97 116 57 129 153 29 124 40
Character -d -u d u c e t h e i d e a s o f a v e r a
Milliseconds 290 145 87 77 67 61 88 200 43 60 85 92 41 74 57 118 90 128 39 61 105 157 145 77 84
Character g e a n d i n s t a n t e -e a n e o u s r a
Milliseconds 78 61 90 76 86 74 52 188 86 119 320 87 92 96 92 347 70 88 561 100 61 78 71 126 108
Character t e s o f c h a g n -n -g n g e , a n d h s
Milliseconds 79 42 144 68 98 94 59 104 68 30 157 91 265 122 82 50 30 102 82 65 87 69 54 264 0
Character o w - -h -s -o -w s h o w t h a t t h e y a r
Milliseconds 163 13 114 682 149 0 0 0 231 63 113 20 106 54 108 19 78 64 84 0 93 61 70 80 95
Character e c l o s l e -e -l e l y r e l a t e d t o
Milliseconds 80 114 103 56 142 63 117 82 309 109 71 124 68 103 114 21 439 50 89 85 120 53 115 34 88
Character t h e s l o p e o f a c u r v e a t a
Milliseconds 74 50 71 62 345 84 145 161 92 65 134 85 52 56 129 9 126 36 144 54 91 108 85 87 105
Character p o i n t P o n t h e c u v -v r v e .
Milliseconds 141 153 181 247 44 58 133 165 132 73 153 79 107 99 28 37 140 116 76 385 112 181 45 90 101
Character W e g i v e p r e c i v -v s e d e v e l o p
Milliseconds 102 89 100 94 92 84 62 80 317 82 81 136 139 122 229 64 105 305 159 120 109 87 100 164 153
Character m e n t s o f t h e s e i m p o r r t a -a -t
Milliseconds 292 85 83 49 107 93 242 68 272 113 83 78 85 84 70 67 69 200 147 43 152 6 91 209 162
Character -r t a n t c o n c e t p -p -t p t s i n t h e
Milliseconds 137 88 109 127 43 96 114 40 87 104 18 413 116 239 131 68 54 94 91 57 51 96 87 59 62
Character n e x t h c -c -h c h a p t e r , b u t f o
Milliseconds 65 170 55 175 190 84 121 60 185 147 79 72 99 86 263 123 64 79 86 84 104 68 77 76 55
Character r n o w e -e w e u s e a n i n f o r m a
Milliseconds 104 82 31 129 30 93 137 347 147 52 85 103 90 37 109 82 73 61 116 74 99 322 82 97 118
Character l a p p r o a c h s o y o u l w i -i -w -
Milliseconds 60 114 160 95 116 84 122 55 142 85 122 153 77 89 111 58 74 91 12 126 84 195 149 162 95
Character i -i - -l w i l l s e e h o w t h e y l e
Milliseconds 318 234 158 131 67 82 47 130 128 17 80 96 132 102 89 116 58 58 82 18 99 55 49 137 43
Character a d n a t r u a -a -u -r u r a l l y t o t h e
Milliseconds 112 19 145 183 124 61 156 42 157 192 155 152 36 66 84 68 121 36 89 109 23 83 71 56 58
Character m a i n m o i -i -o -m i d e a o - d -d f t
Milliseconds 79 47 146 5 73 93 163 43 3 252 164 157 35 66 75 43 134 110 130 360 78 263 90 77 85
Character h i s c h a p t e r , t h e m -m l i m i t .
Milliseconds 22 36 99 51 189 92 90 87 68 91 72 92 78 87 63 291 63 125 236 60 220 80 109 158 130
Character T h e i d e a o d f a -a - -f -d f a l i
Milliseconds 137 137 92 55 51 108 30 84 56 115 141 77 0 57 29 287 174 159 137 194 61 123 94 65 172
Character m p l -l -p i y p l -l -p - -y t p l a y s a f
Milliseconds 84 170 168 199 143 150 131 77 79 140 222 170 154 161 39 45 48 139 55 219 554 69 136 118 62
Character u n -n -u o u n d a t i o n a l r o l e t h r o
Milliseconds 42 52 235 145 34 225 102 105 105 105 29 142 57 85 81 79 91 46 122 63 81 80 63 97 58
Character u g h o u t c a l c u l u s .
Milliseconds 52 60 65 129 34 51 64 301 91 53 92 117 235 104 55 62
WPM Timing
Seconds WPM
2.42 29.81
4.83 81.97
7.25 71.21
9.66 74.52
12.08 69.55
14.49 75.35
16.91 85.88
19.32 83.84
21.74 89.98
24.15 88.43
26.57 84.01
28.98 80.73
31.4 81.78
33.82 85.52
36.23 83.47
38.65 82.6
41.06 82.71
43.48 81.97
45.89 80.28
48.31 80.98
50.72 83.28
53.14 83.78
55.55 83.16
57.97 82.8
60.38 83.66
62.8 83.12
65.22 82.07
67.63 84.1
70.05 83.6
72.46 84.29
74.88 83.98
77.29 83.99
79.71 85.21
82.12 85.92
84.54 86.02
86.95 85.7
89.37 85.67
91.78 85.64
94.2 85.73
96.62 86.45
99.03 87
101.45 85.88
103.86 86.19
106.28 86.6
108.69 86.78
111.11 86.94
113.52 86.15
115.94 85.08
118.35 85.27
120.77 85.85