Jacob (thundermcking)

Race #966

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Official speed 127.35 wpm (81.41 seconds elapsed during race)
Without ending ping 127.89 wpm (344 ms delay sending score to TypeRacer’s server)
Timerless 128.46 wpm (358 ms elapsed before first character typed; 80.71 seconds elapsed during race)
Timerless minus one 128.31 wpm, ignoring the first character typed
Race Start December 1, 2024 7:05:14am UTC
Race Finish December 1, 2024 7:06:35am UTC
Outcome Win (1 of 3)
Opponents 2. kattumanidhan (116.63 wpm)
Accuracy 98.4%
Points 343.83
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 tffalling object chnge ange as a function of time/ ? how doesHow does the level of watter 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 instrucuments help us see more and more. In this section we introduce the ideas of average and instantaneous rates of dchange, and show that they are closely related to the slope of a curve at a opoint P on the curve. We give precise developments of these important concepts in th nee next chapter, ubut nfor now we use nan informal approach so you will see how theyy l lead naturally to the main idea of this chapter, the limit. the iThe idea of a limit plays a foundational role rthroughout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 358 148 83 101 128 120 117 118 49 67 78 57 69 65 100 50 127 141 77 70 51 63 48 34 72
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 81 65 165 69 86 81 88 50 128 145 102 103 71 115 131 117 33 167 93 57 65 111 38 94 41
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 128 39 117 43 122 66 63 76 73 58 86 79 111 54 156 33 144 40 142 40 101 96 75 107 119
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 50 149 66 98 53 77 85 148 70 84 47 38 85 97 63 86 52 84 107 68 73 94 67 39 83
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 74 46 77 86 65 60 40 63 155 84 86 59 120 63 57 77 41 77 68 65 82 39 108 59 110
Character d o f a t f -f -t f a l l i n g o b j e c t
Milliseconds 165 89 75 40 62 85 54 145 147 170 102 119 44 53 132 101 83 66 68 55 95 55 74 156 141
Character c h n g e - -e -g -n a n g e a s a f u n c
Milliseconds 54 120 52 146 69 67 149 194 108 86 127 150 66 119 47 87 66 104 80 64 49 83 82 137 66
Character t i o n o f t i m e / - -/ ? h o w d o e
Milliseconds 130 41 60 69 66 61 82 50 80 62 65 79 169 334 201 99 222 253 513 0 0 0 0 140 150
Character s -d -o -e -s -h -o -w - H o w d o e s t h e l e v
Milliseconds 42 367 0 0 0 83 0 0 0 391 110 82 50 89 54 91 59 38 69 51 54 57 62 108 95
Character e l o f w a t t -t e r i n a b a r r e l
Milliseconds 70 101 65 84 67 51 111 24 211 163 234 183 85 110 84 35 67 66 67 90 66 148 117 86 102
Character c h a n g e a s a f u n c t i o n o f
Milliseconds 26 252 46 55 78 69 53 99 48 69 100 52 66 85 101 125 91 111 37 69 57 67 73 97 51
Character t h e a m o u n t o f l i q u i d p o u r
Milliseconds 82 61 75 65 94 90 115 85 169 99 64 68 98 32 90 97 109 72 65 130 55 95 51 173 130
Character e d i n t o i t ? W e s e e c h a n g e
Milliseconds 77 128 76 56 77 68 80 69 87 99 334 232 137 146 164 88 200 116 92 75 76 48 92 64 55
Character o c c u r r i n g i n n e a r l y e v e r
Milliseconds 66 49 97 114 105 86 129 109 73 52 67 70 62 66 80 86 49 67 72 88 74 54 44 150 56
Character y t h i n g w e o b s e r v e i n t h e
Milliseconds 110 73 112 67 82 101 79 60 59 67 53 84 147 54 49 166 49 81 65 81 35 70 83 39 76
Character w o r l d a n d u n i v e r s e , a n d p
Milliseconds 55 49 36 132 85 78 59 58 133 96 151 183 90 64 154 66 98 68 93 32 72 66 48 81 87
Character o w e r f u l m o d e r n i n s t r u c -c -u u
Milliseconds 37 82 48 18 133 12 64 84 153 56 78 150 0 84 43 58 66 97 52 137 116 91 218 91 744
Character m e n t s h e l p u s s e e m o r e a n
Milliseconds 151 80 75 79 39 93 49 94 72 166 119 163 82 66 88 149 119 54 65 60 8 50 64 64 51
Character d m o r e . I n t h i s s e c t i o n w
Milliseconds 71 57 36 68 35 63 85 21 143 99 51 82 73 44 98 68 70 66 141 129 46 54 32 63 84
Character e i n t r o d u c e t h e i d e a s o f
Milliseconds 53 81 84 65 101 122 47 118 85 63 150 63 70 38 65 41 77 70 120 55 99 102 52 83 61
Character a v e r a g e a n d i n s t a n t a n e o u s
Milliseconds 47 89 139 41 132 36 101 55 75 42 77 66 50 71 48 59 89 118 83 117 164 121 137 41 100
Character r a t e s o f d -d c h a n g e , a n d s
Milliseconds 69 81 101 70 80 61 69 55 50 76 91 294 184 0 0 65 49 422 0 0 0 0 0 71 0
Character h o w t h a t t h e y a r e c l o s e l y
Milliseconds 90 39 54 87 80 80 46 51 70 62 59 49 89 52 52 47 83 71 68 70 124 68 49 53 103
Character r e l a t e d t o t h e s l o p e o f
Milliseconds 59 77 35 65 82 50 83 129 68 95 36 79 78 50 97 49 97 87 148 104 110 52 49 47 88
Character a c u r v e a t a o -o p o i n t P o n
Milliseconds 21 93 51 107 59 150 68 55 98 159 133 52 65 135 263 207 49 187 100 77 101 119 148 121 65
Character t h e c u r v e . W e g i v e p r e c i
Milliseconds 61 67 67 23 84 65 66 81 133 70 62 38 131 137 108 72 86 74 71 54 79 106 29 163 39
Character s e d e v e l o p m e n t s o f t h e s e
Milliseconds 123 66 90 70 129 133 51 87 145 31 280 100 55 81 42 75 54 81 85 51 34 71 59 102 17
Character i m p o r t a n t c o n c e p t s i n t h
Milliseconds 79 79 76 65 55 117 90 51 107 95 84 62 72 34 134 65 83 48 84 51 77 41 59 62 108
Character n e -e -n - e n e x t c h a p t e r , u -u b u
Milliseconds 70 95 151 89 115 131 86 48 86 103 107 85 120 43 75 65 87 113 52 61 74 131 313 154 52
Character t n -n f o r n o w w e u s e n -n a n i
Milliseconds 87 58 88 223 88 86 77 36 74 45 65 432 87 49 94 54 85 33 113 201 222 61 96 68 43
Character n f o r m a l a p p r o a c h s o y o u w
Milliseconds 78 54 92 76 69 95 126 71 129 70 66 99 74 126 69 108 27 114 67 45 205 110 70 51 154
Character i l l s e e h o w t h e y y l -l - -y l e
Milliseconds 67 117 112 52 62 121 116 58 37 53 37 64 72 32 95 77 126 0 149 205 106 106 175 40 69
Character a d n a t u r a l l y t o t h e m a i n
Milliseconds 53 108 68 68 79 53 66 71 52 59 90 117 61 46 70 55 39 89 21 91 50 103 49 72 67
Character i d e a o f t h i s c h a p t e r , t h e
Milliseconds 65 83 117 54 63 48 78 49 77 47 40 54 71 106 52 74 63 95 159 36 225 73 89 62 60
Character l i m i t . t h e i -i -t -h -e - T h e i d e
Milliseconds 54 41 84 60 101 145 86 39 243 88 65 82 52 231 98 0 0 0 413 90 47 85 46 31 155
Character a o f a l i m i t p l a y s a f o u n
Milliseconds 63 75 64 83 55 65 64 93 78 50 115 101 95 72 180 67 93 68 84 41 55 90 119 0 168
Character d a t i o n a l r o l e r -r t h r o u g h o u
Milliseconds 46 63 425 0 0 0 0 0 0 105 0 143 126 85 298 233 90 47 82 39 75 90 68 90 89
Character t c a l c u l u s .
Milliseconds 86 45 115 65 24 101 42 87 73 91 70
WPM Timing
Seconds WPM
1.63 103.18
3.26 125.29
4.88 127.74
6.51 130.81
8.14 132.66
9.77 137.57
11.4 138.97
13.03 133.58
14.65 125.29
16.28 128.97
17.91 118.59
19.54 111.16
21.17 114.52
22.8 113.71
24.42 115.95
26.05 117.46
27.68 118.78
29.31 116.28
30.94 118.3
32.57 120.13
34.19 122.13
35.82 122.61
37.45 123.68
39.08 120.68
40.71 121.75
42.33 123.59
43.96 124.47
45.59 126.08
47.22 126.3
48.85 127.01
50.48 128.61
52.1 129.43
53.73 128.41
55.36 128.32
56.99 128.87
58.62 129.18
60.25 129.87
61.87 128.78
63.5 127.93
65.13 127.5
66.76 127.26
68.39 127.39
70.02 126.66
71.64 127.8
73.27 128.56
74.9 127.85
76.53 127.32
78.16 127.59
79.79 127.24
81.41 127.35