quite fast (edonn)

Race #13701

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Official speed 120.11 wpm (86.32 seconds elapsed during race)
Without ending ping 120.34 wpm (164 ms delay sending score to TypeRacer’s server)
Timerless 120.87 wpm (382 ms elapsed before first character typed; 85.78 seconds elapsed during race)
Timerless minus one 120.73 wpm, ignoring the first character typed
Race Start January 9, 2024 9:24:33am UTC
Race Finish January 9, 2024 9:25:59am UTC
Outcome Win (1 of 3)
Opponents 3. hirohero89 (98.05 wpm)
Accuracy 99.1%
Points 324.29
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 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 occuring in ring in nearly aeverything 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 instatntatnneous rates of change, and show that they are closely related to the slop e of a curve at a point P on the curve. We give precise developments of these important concepts in the next chapter, fobut 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 calcullusus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 382 595 143 162 103 192 253 155 50 89 68 68 90 66 158 56 106 170 108 118 77 18 92 326 145
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 86 104 78 115 96 39 175 159 78 164 81 139 59 119 61 68 32 103 30 40 92 12 72 68 106
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 111 120 100 53 34 121 61 64 63 59 59 72 69 100 210 62 104 84 107 126 83 107 76 164 45
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 105 80 54 96 54 48 39 158 78 81 71 71 47 107 132 100 112 79 5 110 65 134 31 53 140
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 79 52 108 61 62 90 98 55 202 103 61 120 86 95 90 68 47 122 56 126 60 121 117 84 116
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 185 162 170 130 80 88 39 142 58 80 94 57 107 27 104 213 112 78 81 157 99 87 159 106 79
Character n g e a s a f u n c t i o n o f t i m e
Milliseconds 55 39 79 147 93 68 94 82 56 80 198 234 121 152 59 16 30 87 72 87 36 132 24 55 55
Character ? H o w d o e s t h e l e v e l o f w
Milliseconds 257 30 270 351 134 92 123 112 87 37 60 147 52 90 56 54 79 130 90 28 41 123 36 83 297
Character a t e r i n a b a r r e l c h a n g e a
Milliseconds 38 105 88 79 64 106 72 43 82 58 103 121 80 135 61 132 55 107 93 63 74 19 82 100 80
Character s a f u n c t i o n o f t h e a m o u n
Milliseconds 62 66 87 43 97 110 133 72 133 67 35 20 81 81 53 41 160 40 115 43 180 73 71 95 152
Character t o f l i q u i d p o u r e d i n t o i
Milliseconds 123 53 68 84 55 128 54 236 60 42 129 73 208 193 53 131 159 169 107 116 76 172 53 82 88
Character t ? W e s e e c h a n g e o c c u r i n g
Milliseconds 104 235 35 241 176 56 281 64 141 68 136 96 98 61 35 135 53 81 72 127 99 102 64 36 93
Character i n - -n -i - -g -n -i r i n g i n n e a r l y
Milliseconds 36 74 47 90 217 246 33 35 32 34 34 418 78 56 111 95 104 40 98 105 65 54 30 93 34
Character a -a e v e r y t h i n g w e o b s e r v e
Milliseconds 40 142 298 56 109 119 53 75 73 69 47 86 22 101 58 55 85 34 80 135 57 22 174 79 65
Character i n t h e w o r l d a n d u n i v e r s e
Milliseconds 52 65 56 72 122 60 100 78 104 82 80 103 56 90 82 115 32 79 156 43 58 200 57 55 105
Character , a n d p o w e r f u l m o d e r n i n s
Milliseconds 95 32 155 76 123 46 87 39 79 56 89 151 526 43 92 265 44 99 136 56 62 64 137 53 101
Character t r u m e n t s h e l p u s s e e m o r e
Milliseconds 79 135 80 168 104 47 95 84 87 64 87 96 63 47 57 138 51 129 88 132 74 95 78 77 41
Character a n d m o r e . I n t h i s s e c t i o
Milliseconds 32 139 55 93 41 69 68 109 33 98 58 161 125 54 200 92 55 56 104 113 60 186 125 43 37
Character n w e i n t r o d u c e t h e i d e a s
Milliseconds 32 39 98 59 73 167 35 78 157 22 133 84 97 138 118 99 59 66 31 57 106 142 57 46 163
Character o f a v e r a g e a n d i n s t a t -t n t a
Milliseconds 81 95 72 182 154 113 72 20 266 154 146 143 79 78 67 62 61 74 73 77 92 599 201 321 89
Character t n -n -t n e o u s r a t e s o f c h a n g e
Milliseconds 72 302 271 100 155 102 125 18 93 89 159 80 103 55 122 200 105 66 82 123 96 31 130 34 91
Character , a n d s h o w t h a t t h e y a r e
Milliseconds 122 33 51 99 55 73 63 80 49 56 100 124 96 37 66 62 132 37 91 53 38 73 56 33 57
Character c l o s e l y r e l a t e d t o t h e s l
Milliseconds 138 34 114 72 31 76 46 48 25 55 120 67 55 29 157 61 80 57 56 64 54 74 72 136 241
Character o p - e o f a c u r v e a t a p o i
Milliseconds 337 72 174 344 96 57 65 44 82 38 83 183 33 97 189 97 83 99 50 54 106 40 145 20 36
Character n t P o n t h e c u r v e . W e g i v
Milliseconds 27 99 74 302 103 113 47 87 117 70 103 62 133 53 82 179 93 75 45 159 149 31 149 62 130
Character e p r e c i s e d e v e l o p m e n t s o f
Milliseconds 71 28 60 65 63 177 88 83 53 70 243 160 83 108 27 149 60 148 88 88 134 87 120 58 105
Character t h e s e i m p o r t a n t c o n c e p t s
Milliseconds 63 97 54 57 112 77 13 113 66 71 57 83 138 38 82 87 101 100 60 56 59 176 70 73 72
Character i n t h e n e x t c h a p t e r , f o -o
Milliseconds 82 34 66 70 55 103 55 160 103 81 175 129 64 144 96 79 120 54 57 144 114 54 93 101 232
Character -f b u t f o r n o w w e u s e a n i n
Milliseconds 110 242 122 51 117 61 105 27 40 95 57 53 107 80 40 96 73 93 59 89 114 90 88 100 42
Character f o r m a l a p p r o a c h s o y o u w i
Milliseconds 96 90 111 37 148 80 61 204 53 108 132 29 124 129 27 57 194 81 55 323 93 62 65 73 68
Character l l s e e h o w t h e y l e a d n a t u
Milliseconds 162 82 65 502 54 146 38 104 75 73 93 151 58 91 42 46 94 54 56 122 65 88 85 73 86
Character r a l l y t o t h e m a i n i d e a o f
Milliseconds 91 71 105 105 51 84 119 69 58 99 107 56 50 117 110 53 64 58 199 121 301 59 105 63 84
Character t h i s c h a p t e r , t h e l i m i t .
Milliseconds 43 177 55 30 66 61 142 76 108 93 62 88 108 92 77 129 55 94 47 34 79 46 83 143 94
Character T h e i d e a o f a l i m i t p l a y
Milliseconds 52 167 131 33 73 82 55 130 54 82 71 89 55 55 85 34 106 46 99 86 73 73 144 54 129
Character s a f o u n d a t i o n a l r o l e t h r
Milliseconds 61 105 96 71 137 55 50 153 105 78 84 78 14 37 271 79 86 322 69 144 71 74 193 77 104
Character o u g h o u t c a l c u l l u s -s -u -l u s .
Milliseconds 18 53 83 54 55 83 55 137 89 63 36 133 79 90 254 168 128 283 117 105 136 85 84
WPM Timing
Seconds WPM
1.73 41.7
3.45 79.93
5.18 88.04
6.91 107.74
8.63 111.21
10.36 117.01
12.08 119.16
13.81 118.16
15.54 118.16
17.26 119.55
18.99 117.53
20.72 118.74
22.44 121.37
24.17 123.13
25.9 121.87
27.62 120.77
29.35 120.21
31.08 114.69
32.8 114.87
34.53 117.47
36.25 118.49
37.98 117.85
39.71 117.86
41.43 119.32
43.16 119.55
44.89 120.3
46.61 120.22
48.34 118.91
50.07 116.25
51.79 116.54
53.52 118.39
55.25 119.9
56.97 118.37
58.7 118.78
60.42 118.96
62.15 119.13
63.88 119.67
65.6 120.36
67.33 119.95
69.06 119.9
70.78 120.2
72.51 119.98
74.24 119.94
75.96 120.53
77.69 120.48
79.42 120.73
81.14 121.42
82.87 121.49
84.59 121.71
86.32 120.11