ben (risns)

Race #1353

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Official speed 110.19 wpm (94.09 seconds elapsed during race)
Without ending ping 110.57 wpm (322 ms delay sending score to TypeRacer’s server)
Timerless 110.93 wpm (308 ms elapsed before first character typed; 93.46 seconds elapsed during race)
Timerless minus one 110.80 wpm, ignoring the first character typed
Race Start September 27, 2023 7:41:51pm UTC
Race Finish September 27, 2023 7:43:26pm UTC
Outcome Win (1 of 4)
Opponents 2. rainbowarsenal (95.62 wpm)
3. staltmors (83.14 wpm)
Accuracy 96.8%
Points 297.52
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 stotool that helps us understand hoa a w a change in one quanitytity is related to a change in another. How does thes s speed of a falling object change as a function fo of time? How does the level of water in a barrel change as a function of teh ahe amoiuountunt of liquid pourdeded into intt? We se e change occurring in nearly everything we observe in the world and universe, an pd powerful modern instruments help us see more and more. In this section we intorcroduce the idea s of average and instaneoutaneous rates of change, and show that they are closely related to the slope of the ca 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 informaapl approach so you will see how they lead naturally ot thto the main deaidea of this chapter, the limit; T. The idea of a limit aplays a foundational role throughout clacalculus.
Timing
Character C a l c u l u s i s a s t o -o -t -s t o o l
Milliseconds 308 72 113 98 129 152 171 86 65 111 88 62 110 68 109 81 57 274 152 141 99 72 130 149 47
Character t h a t h e l p s u s u n d e r s t a n d
Milliseconds 47 108 22 69 47 100 64 117 40 82 49 116 153 71 170 147 69 103 56 123 21 115 114 36 95
Character h o a a - -a - -a w a c h a n g e i n o
Milliseconds 116 12 108 41 138 29 198 123 141 147 30 44 111 32 157 70 72 108 76 54 56 95 38 50 157
Character n e q u a n i t y -y -t -i t i t y i s r e l a
Milliseconds 75 34 90 280 81 83 77 168 52 101 174 117 145 104 50 105 36 79 110 77 90 141 78 47 100
Character t e d t o a c h a n g e i n a n o t h e
Milliseconds 54 75 90 94 110 19 66 117 49 333 86 52 109 124 85 108 169 69 72 21 170 44 73 57 83
Character r . H o w d o e s t h e s s -s - -s s p e
Milliseconds 62 117 33 194 137 105 71 69 82 89 75 68 72 72 75 12 74 69 204 278 155 56 47 123 61
Character e d o f a f a l l i n g o b j e c t c h
Milliseconds 133 98 43 144 93 88 167 78 115 112 108 128 168 18 53 69 56 203 193 97 50 161 63 119 74
Character a n g e a s a f u n c t i o n f o - -o -f
Milliseconds 39 110 19 44 88 77 37 79 59 84 163 70 51 73 160 60 39 132 37 146 12 140 235 124 148
Character o f t i m e ? H o w d o e s t h e l e v
Milliseconds 50 100 17 122 54 22 88 245 47 263 166 101 51 101 65 57 47 77 53 55 87 85 182 67 47
Character e l o f w a t e r i n a b a r r e l c
Milliseconds 116 65 72 148 45 83 66 65 51 110 39 69 121 38 47 53 121 181 55 60 146 195 83 50 224
Character h a n g e a s a f u n c t i o n o f t e
Milliseconds 94 50 104 29 50 74 62 44 82 232 227 155 166 55 54 143 44 58 119 41 129 0 124 38 129
Character h a -a - -h -e h e a m o i u -u -i o u n t -t -n -u -o
Milliseconds 7 100 93 195 126 155 126 155 68 79 86 120 129 55 0 335 139 173 43 151 46 202 113 149 123
Character u n t o f l i q u i d p o u r d e d -d -e -d e
Milliseconds 221 60 65 86 108 76 45 99 413 80 78 72 40 100 368 181 104 64 161 50 82 189 133 142 27
Character d i n t o i n t -t -n t ? W e s e - e c
Milliseconds 17 96 132 32 86 97 51 134 42 128 178 132 59 225 102 206 111 153 121 50 194 243 45 75 98
Character h a n g e o c c u r r i n g i n n e a r l y
Milliseconds 64 43 104 49 52 51 141 94 134 145 42 134 107 52 38 92 75 54 60 180 94 43 59 85 115
Character e v e r y t h i n g w e o b s e r v e i n
Milliseconds 48 143 137 67 34 57 113 67 57 63 28 54 115 34 80 184 147 104 37 51 160 131 79 117 18
Character t h e w o r l d a n d u n i v e r s e ,
Milliseconds 72 80 82 67 85 77 70 60 89 74 59 67 65 92 53 97 37 139 78 141 35 152 76 111 50
Character a n p -p - d p o w e r f u l m o d e r n i
Milliseconds 146 71 152 136 275 133 116 67 117 60 34 30 38 156 50 161 77 183 43 123 103 59 70 57 93
Character n s t r u m e n t s h e l p u s s e e m o
Milliseconds 50 62 30 149 42 144 108 73 62 99 53 127 107 70 20 57 170 73 82 119 52 154 93 103 71
Character r e a n d m o r e . I n t h i s s e c t
Milliseconds 33 45 59 97 60 71 51 90 27 42 33 113 28 205 156 42 56 90 37 56 70 325 36 35 216
Character i o n w e i n t o r c -c -r -o r o d u c e t h
Milliseconds 61 44 126 55 49 29 83 99 41 36 165 9 194 173 139 139 52 83 100 99 52 121 86 185 53
Character e i d e a - s o f a v e r a g e a n d
Milliseconds 71 68 57 69 53 66 118 291 52 80 54 119 99 341 99 398 39 123 62 60 29 171 53 75 68
Character i n s t a n e o u -u -o -e t a n e o u s r a t e s
Milliseconds 67 66 56 61 118 92 151 114 71 201 133 125 39 103 67 116 69 66 78 100 177 104 97 74 76
Character o f c h a n g e , a n d s h o w t h a t
Milliseconds 39 230 70 97 175 81 32 123 11 68 93 36 69 99 70 72 72 93 27 94 31 106 58 53 55
Character t h e y a r e c l o s e l y r e l a t e d
Milliseconds 52 94 59 84 69 34 155 71 51 69 179 79 161 45 170 115 102 78 143 69 55 100 59 118 70
Character t o t h e s l o p e o f t h e c -c - -e
Milliseconds 36 156 12 76 139 56 68 77 121 48 165 127 56 78 112 48 59 87 46 41 69 85 149 135 148
Character -h -t a c u r v e a t a p o i n t P o n
Milliseconds 160 139 23 106 116 116 49 144 44 43 154 74 55 77 77 232 121 185 148 48 77 121 107 124 137
Character t h e c u r v e . W e g i v e p r e c i
Milliseconds 75 20 99 31 92 234 80 71 151 51 71 44 140 102 66 159 57 93 49 36 171 75 80 130 127
Character s e d e v e l o p m e n t s o f t h e s e
Milliseconds 34 67 59 104 96 129 76 68 127 69 172 72 72 48 79 59 111 25 99 59 64 36 86 121 2
Character i m p o r t a n t c o n c e p t s i n t h e
Milliseconds 104 44 138 71 100 54 116 81 77 76 220 85 37 65 90 54 89 88 75 115 41 58 46 74 72
Character n e x t c h a p t e r , b u t f o r n o
Milliseconds 54 99 75 167 124 49 185 67 84 81 52 90 45 108 41 150 49 58 75 117 81 86 62 146 35
Character w w e u s e a n i n f o r m a a p -p -a l
Milliseconds 96 57 102 20 88 115 40 62 56 167 117 77 162 56 105 103 68 79 101 222 78 219 119 105 46
Character a p p r o a c h s o y o u w i l l s e e
Milliseconds 86 84 147 76 87 71 86 94 42 237 63 37 99 72 29 164 135 51 143 122 60 129 36 140 42
Character h o w t h e y l e a d n a t u r a l l y o
Milliseconds 115 69 80 49 76 70 67 88 29 145 90 31 49 63 99 88 41 78 109 29 49 151 61 14 168
Character t t h -h -t - -t -o t o t h e m a i n d e a -a
Milliseconds 0 66 144 24 189 121 146 161 141 92 65 50 77 76 56 47 281 81 87 45 81 120 73 70 200
Character -e -d i d e a o f t h i s c h a p t e r , t
Milliseconds 132 146 88 60 53 40 48 171 60 119 129 67 51 50 89 123 92 46 117 48 108 38 66 42 87
Character h e l i m i t ; T -T - -; . T h e i d e a
Milliseconds 65 77 63 108 173 54 107 72 114 61 111 128 129 151 124 46 91 108 44 67 104 42 61 55 28
Character o f a l i m i t a -a p l a y s a f o u n
Milliseconds 129 31 93 39 70 147 170 19 130 70 123 5 337 244 27 36 105 114 75 82 101 113 101 54 154
Character d a t i o n a l r o l e t h r o u g h o u t
Milliseconds 18 166 50 86 51 102 112 67 57 77 50 142 73 93 225 79 79 53 43 79 91 67 76 30 79
Character c l a c -c -a -l a l c u l u s .
Milliseconds 113 93 31 162 187 129 145 66 110 86 108 160 155 80 1014
WPM Timing
Seconds WPM
1.88 89.27
3.76 95.65
5.65 97.78
7.53 102.03
9.41 96.93
11.29 100.97
13.17 105.67
15.05 102.82
16.94 103.44
18.82 107.13
20.7 104.93
22.58 108.94
24.46 110.86
26.35 110.23
28.23 105.43
30.11 102.03
31.99 99.78
33.87 98.49
35.75 98.67
37.64 101.07
39.52 102.94
41.4 104.64
43.28 103.97
45.16 105.75
47.05 107.38
48.93 108.4
50.81 107.93
52.69 107.04
54.57 106.21
56.46 106.92
58.34 108.61
60.22 109.4
62.1 108.21
63.98 108.22
65.86 108.77
67.75 109.47
69.63 110.65
71.51 111.43
73.39 112.33
75.27 111.91
77.16 112.14
79.04 112.96
80.92 111.82
82.8 111.45
84.68 112.23
86.56 111.87
88.45 111.66
90.33 112.12
92.21 111.66
94.09 110.19