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Race #14

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Official speed 87.05 wpm (119.10 seconds elapsed during race)
Without ending ping 87.40 wpm (333 ms delay sending score to TypeRacer’s server)
Timerless 87.52 wpm (171 ms elapsed before first character typed; 118.60 seconds elapsed during race)
Timerless minus one 87.42 wpm, ignoring the first character typed
Race Start February 4, 2024 10:57:00pm UTC
Race Finish February 4, 2024 10:58:59pm UTC
Outcome No win (5 of 5)
Opponents 1. grand_54 (109.80 wpm)
2. jpen369 (94.22 wpm)
4. yesterdaysjamm (89.84 wpm)
Accuracy 97.6%
Points 235.03
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 hchange in one quality uantity is releateelated 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 puoured into it? We see change occurring in nearly evertyuththithiung wverything we observe in the world and universe, and powerful moedern instruments help us see more and more. In this section we uintntroduce the iideas of average and instantaneous ratets oates of change, and show that they are closely related to the slope of a curve at a point pP on teh cuhe curevve. We give prescise developments of thse ieseehese important concepts in ytthe next cehapter, but for now we use an informatl 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. thr1ole thole 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 171 658 57 257 91 164 104 177 107 124 52 65 101 65 127 99 102 216 26 90 90 49 34 67 150
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 117 108 269 135 139 149 60 132 420 149 83 124 57 152 649 92 149 133 92 151 107 19 99 69 82
Character h -h c h a n g e i n o n e q u a l i t y -u
Milliseconds 240 327 17 58 122 59 93 75 101 90 75 91 392 117 60 106 290 86 124 101 49 120 114 150 1096
Character -a -l -i -t -y - u a n t i t y i s r e l e a t e -e
Milliseconds 0 0 0 0 0 0 105 108 109 100 43 124 105 133 133 59 92 267 84 160 66 43 139 84 475
Character -l -e -a -t -e e l a t e d t o a c h a n g e i
Milliseconds 0 0 0 0 0 49 193 68 131 68 124 107 69 64 75 43 125 65 84 115 39 96 51 116 91
Character n a n o t h e r . H o w d o e s t h e s
Milliseconds 75 42 84 125 152 91 57 43 42 110 63 162 96 120 40 133 92 67 76 66 76 64 49 68 134
Character p e e d o f a f a l l i n g o b j e c t
Milliseconds 107 68 466 167 151 107 66 67 59 76 139 77 110 124 95 55 32 74 110 108 186 100 144 146 77
Character c h a n g e a s a f u n c t i o n o f t
Milliseconds 150 90 77 105 51 50 152 98 141 119 40 111 75 159 140 23 124 84 58 27 90 135 42 81 66
Character i m e ? H o w d o e s t h e l e v e l o
Milliseconds 174 59 43 209 123 192 109 126 24 183 118 60 64 111 82 57 58 59 134 58 149 32 167 119 124
Character f w a t e r i n a b a r r e l c h a n g
Milliseconds 84 64 127 128 139 85 630 119 150 75 65 52 124 83 127 113 119 152 131 75 199 99 58 88 39
Character e a s a f u n c t i o n o f t h e a m
Milliseconds 85 105 85 149 143 33 126 82 159 151 49 115 109 42 60 74 123 34 83 76 60 81 83 91 103
Character o u n t o f l i q u i d p u -u o u r e d i
Milliseconds 142 59 150 57 192 140 52 105 157 46 318 7 214 202 173 196 150 371 108 27 58 165 161 125 122
Character n t o i t ? W e s e e c h a n g e o c c
Milliseconds 76 51 82 60 123 61 225 76 206 159 108 236 134 120 261 101 109 71 83 53 47 126 134 165 127
Character u r r i n g i n n e a r l y e v e r t -t y u
Milliseconds 94 83 154 184 60 66 85 91 102 121 241 77 101 132 124 119 76 67 138 86 80 287 646 62 31
Character t h -h -t t h i -i -h -t -u t h i u n g w -v -e -r -y -t -h
Milliseconds 51 142 465 151 11 92 199 298 150 151 166 59 89 150 2 26 35 100 140 768 0 0 0 0 0
Character -i -u -n -g - -w v e r y t h i n g w e o b s e r v
Milliseconds 0 0 0 0 0 0 189 143 34 214 142 82 125 70 31 102 74 57 127 327 82 193 104 35 176
Character e i n t h e w o r l d a n d u n i v e r
Milliseconds 131 91 150 18 59 0 132 21 113 32 134 27 147 67 134 94 56 66 68 352 147 284 133 110 75
Character s e , a n d p o w e r f u l m o e -e d e r n
Milliseconds 141 118 339 58 119 90 43 118 155 177 68 40 84 184 122 112 83 197 51 150 433 54 137 25 229
Character i n s t r u m e n t s h e l p u s s e e
Milliseconds 124 100 91 59 164 137 132 165 58 84 24 128 141 107 67 130 62 116 118 83 115 50 137 124 107
Character m o r e a n d m o r e . I n t h i s s e
Milliseconds 110 39 51 31 101 84 65 51 97 62 60 41 31 151 60 214 150 86 9 148 68 64 101 183 167
Character c t i o n w e u i n t -u -n -t n t r o d u c e
Milliseconds 149 152 25 75 48 58 93 52 80 151 27 31 147 678 0 0 75 44 148 77 149 77 190 116 132
Character t h e i -i i d e a s o f a v e r a g e a n
Milliseconds 60 73 77 57 150 317 342 86 157 125 148 145 109 43 72 160 96 127 60 116 150 106 103 100 49
Character d i n s t a n t a n e o u s r a t e t s o -a
Milliseconds 102 50 83 99 165 141 127 107 115 117 216 112 138 75 108 134 101 112 98 91 16 134 125 116 433
Character -t -e -t -s - -o a t e s o f c h a n g e , a n d
Milliseconds 0 0 0 0 0 0 124 108 94 118 146 119 48 86 257 102 88 77 94 30 133 59 92 73 50
Character s h o w t h a t t h e y a r e c l o s e
Milliseconds 70 141 24 109 115 135 57 108 18 51 82 74 108 69 65 75 58 76 66 68 142 99 109 35 164
Character l y r e l a t e d t o t h e s l o p e o
Milliseconds 66 120 138 84 51 117 77 132 89 121 107 66 68 75 41 97 42 111 116 106 119 210 182 131 183
Character f a c u r v e a t a p o i n t p -p P
Milliseconds 25 137 80 133 119 171 48 198 73 201 59 191 78 52 114 124 57 170 40 78 191 238 426 57 252
Character o n t e h c u -c -u -e -h - h e c u r e v -v -e v
Milliseconds 166 66 74 42 116 3 74 142 142 391 0 224 0 0 150 132 184 216 117 103 255 29 525 120 4
Character e . W e g i v e p r e s -s c i s e d e v e
Milliseconds 29 136 160 238 170 117 121 96 83 49 101 138 76 43 144 374 15 82 95 49 157 192 185 201 65
Character l o p m e n t s o f t h s e i -h -s -e - -i e s
Milliseconds 166 166 74 253 163 109 62 149 107 118 67 40 84 84 158 57 167 135 498 0 0 0 0 161 137
Character e e -e -s -e -e h e s e i m p o r t a n t c o n c
Milliseconds 45 83 431 0 0 0 133 59 167 59 192 188 53 119 109 92 122 84 91 57 126 108 83 93 158
Character e p t s i n y t -t t -y h e n e x t c e -e h
Milliseconds 144 106 98 80 122 92 83 67 186 207 242 5 550 120 56 110 124 42 157 145 57 132 193 334 64
Character a p t e r , b u t f o r n o w w e u s e
Milliseconds 117 109 110 131 52 199 59 335 122 65 77 75 127 24 50 132 58 58 77 101 2 481 151 83 125
Character a n i n f o r m a t -t l a p p r o a c h s
Milliseconds 65 158 100 115 122 71 133 123 44 75 65 91 654 300 180 261 100 150 81 116 35 98 127 68 149
Character o y o u w i l l s e e h o w t h e y l
Milliseconds 123 41 136 92 74 32 59 134 150 119 75 63 60 140 134 175 75 59 91 77 89 50 84 59 134
Character e a d n a t u r a l l y t o t h e m a i n
Milliseconds 65 58 187 130 119 61 146 93 60 79 202 240 258 138 147 90 59 24 109 34 118 58 65 175 45
Character i d e a o f t h i s c h a p t e r , t h
Milliseconds 90 123 100 110 99 191 68 59 49 86 48 118 34 88 284 76 58 119 132 76 67 133 42 117 81
Character e l i m i t . T h e i d e a o f a l i
Milliseconds 34 99 152 42 166 55 126 178 150 189 126 27 108 123 59 135 90 291 116 83 126 23 110 166 43
Character m i t p l a y s a f o u n d a t i o n a l
Milliseconds 125 85 106 124 70 150 42 158 49 126 55 110 116 110 48 177 69 104 119 134 54 62 135 201 114
Character r o l e . - t h r -o -l -e -. - -t -h -r 1 o l e t
Milliseconds 107 115 166 20 158 49 525 599 168 180 104 625 0 0 0 0 0 0 0 33 43 149 29 106 46
Character h -r -1 -o -l -e - -h o l e $r -o -l -e - o l e t h r o
Milliseconds 76 400 0 0 0 0 0 0 199 186 33 156 475 0 0 0 0 126 165 60 118 76 105 141 70
Character u g h o u t c a l c u l u s .
Milliseconds 90 400 516 151 64 59 118 126 124 107 142 52 150 134 100 143
WPM Timing
Seconds WPM
2.38 75.56
4.76 83.12
7.15 83.96
9.53 81.86
11.91 72.54
14.29 69.69
16.67 80.6
19.06 84.38
21.44 87.88
23.82 91.18
26.2 92.97
28.58 93.62
30.97 96.49
33.35 94.64
35.73 94.71
38.11 95.4
40.5 92.75
42.88 87.6
45.26 86.43
47.64 88.41
50.02 87.8
52.41 87.7
54.79 88.92
57.17 90.47
59.55 90.27
61.93 89.9
64.32 90.49
66.7 89.42
69.08 91.2
71.46 92.52
73.84 92.46
76.23 92.09
78.61 90.22
80.99 89.79
83.37 89.67
85.75 87.88
88.14 88.5
90.52 87.89
92.9 87.84
95.28 88.28
97.67 87.61
100.05 88.64
102.43 88.92
104.81 89.76
107.19 90.23
109.58 90.79
111.96 90.03
114.34 88.16
116.72 87.39
119.1 87.05