Sophia (小雪） (renissia)

Race #2381

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Official speed 122.92 wpm (84.35 seconds elapsed during race)
Without ending ping 123.09 wpm (118 ms delay sending score to TypeRacer’s server)
Timerless 123.82 wpm (496 ms elapsed before first character typed; 83.73 seconds elapsed during race)
Timerless minus one 123.68 wpm, ignoring the first character typed
Race Start January 23, 2024 4:44:13pm UTC
Race Finish January 23, 2024 4:45:37pm UTC
Outcome Win (1 of 4)
Opponents 3. can_i_kinesis (77.77 wpm)
Accuracy 99.3%
Points 331.88
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 undreerstand 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 ina an 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 hcapthapter, the limit. The idea of a limit plays a foundaitonal oundational 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 496 76 94 96 67 135 114 64 90 44 138 78 87 85 55 55 160 154 80 59 85 78 76 61 43
Character e l p s u s u n d r e -e -r e r s t a n d h o
Milliseconds 136 42 119 75 76 125 89 94 112 148 78 174 0 396 410 130 86 110 82 89 73 110 58 74 110
Character w a c h a n g e i n o n e q u a n t i t
Milliseconds 60 158 130 129 103 96 90 80 74 76 36 48 76 98 45 84 55 66 100 74 124 87 109 78 103
Character y i s r e l a t e d t o a c h a n g e
Milliseconds 70 86 91 103 80 65 56 94 120 64 104 177 63 86 77 100 86 116 52 94 70 103 69 72 25
Character i n a n o t h e r . H o w d o e s t h e
Milliseconds 60 85 70 66 58 109 79 114 62 90 54 110 132 126 39 99 83 97 83 90 42 69 72 110 146
Character s p e e d o f a f a l l i n g o b j e c t
Milliseconds 126 93 103 166 169 34 107 83 118 87 118 62 64 80 168 152 78 40 78 98 70 85 95 166 101
Character c h a n g e a s a f u n c t i o n o f
Milliseconds 98 119 96 75 99 70 67 87 92 102 128 72 92 60 80 158 110 95 33 82 59 45 143 41 89
Character t i m e ? H o w d o e s t h e l e v e l
Milliseconds 84 43 97 80 145 109 153 131 42 88 82 82 112 86 64 79 63 137 15 471 85 118 70 78 71
Character o f w a t e r i n a a -n -a - -a n a b a r
Milliseconds 107 33 89 43 91 66 147 93 52 52 76 100 37 169 755 0 0 0 65 87 86 115 52 137 72
Character r e l c h a n g e a s a f u n c t i o n
Milliseconds 193 64 93 78 100 63 107 85 50 81 93 96 98 95 97 84 64 78 153 97 112 17 77 67 47
Character o f t h e a m o u n t o f l i q u i d p
Milliseconds 136 44 87 79 99 87 62 112 64 128 102 172 81 63 60 128 97 20 160 154 105 102 101 60 78
Character o u r e d i n t o i t ? W e s e e c h a
Milliseconds 93 95 83 69 169 71 88 60 64 104 56 109 73 175 111 201 70 110 97 74 160 111 111 75 93
Character n g e o c c u r r i n g i n n e a r l y e
Milliseconds 90 62 78 41 117 116 153 62 110 156 93 77 51 48 86 67 55 109 74 70 74 20 124 73 68
Character v e r y t h i n g w e o b s e r v e i n t
Milliseconds 112 140 67 70 112 71 144 90 35 70 96 77 103 84 56 153 45 114 160 106 82 91 53 70 60
Character h e w o r l d a n d u n i v e r s e , a n
Milliseconds 69 106 77 54 107 79 97 65 80 72 104 72 61 65 165 103 72 114 88 93 76 88 94 78 76
Character d p o w e r f u l m o d e r n i n s t r u m
Milliseconds 87 59 214 104 50 22 77 149 53 90 80 113 74 36 164 48 68 108 58 86 60 43 143 44 174
Character e n t s h e l p u s s e e m o r e a n d
Milliseconds 110 64 78 86 40 62 141 35 126 116 60 116 90 104 57 158 79 58 68 102 65 105 88 90 86
Character m o r e . I n t h i s s e c t i o n w e
Milliseconds 60 56 95 37 62 124 76 151 160 84 39 68 87 63 97 110 61 185 113 25 72 60 74 58 76
Character i n t r o d u c e t h e i d e a s o f a
Milliseconds 93 84 82 39 147 56 131 68 127 154 79 82 80 107 26 137 84 155 62 155 82 100 100 67 106
Character v e r a g e a n d i n s t a n t a n e o u s
Milliseconds 107 138 76 70 114 97 81 102 114 86 46 72 80 73 45 104 98 767 342 124 109 105 76 74 77
Character r a t e s o f c h a n g e , a n d s h o w
Milliseconds 96 88 99 109 95 46 102 92 82 124 37 139 62 107 71 42 90 86 110 56 94 101 58 100 73
Character t h a t t h e y a r e c l o s e l y r e
Milliseconds 51 94 61 112 70 82 112 32 160 59 98 65 87 68 92 118 58 155 104 45 55 140 64 66 80
Character l a t e d t o t h e s l o p e o f a c
Milliseconds 40 105 83 87 181 60 86 78 95 66 59 103 80 100 28 171 75 58 86 99 161 106 120 110 135
Character u r v e a t a p o i n t P o n t h e
Milliseconds 110 97 152 114 72 100 64 114 104 82 88 71 68 77 34 72 158 142 72 88 84 60 62 106 104
Character c u r v e . W e g i v e p r e c i s e d e
Milliseconds 132 157 0 199 77 63 110 228 70 107 73 74 112 72 136 0 102 92 181 97 122 46 102 116 150
Character v e l o p m e n t s o f t h e s e i m p o r
Milliseconds 110 96 22 176 122 70 148 80 96 98 46 126 70 106 72 70 93 125 90 77 61 79 88 78 64
Character t a n t c o n c e p t s i n t h e n e x t
Milliseconds 146 74 84 96 84 146 58 84 56 160 58 85 85 60 74 82 56 78 56 130 79 47 96 188 134
Character c h a p t e r , b u t f o r n o w w e
Milliseconds 86 124 82 108 82 78 130 80 68 96 88 86 102 86 116 106 68 70 58 88 44 124 110 82 104
Character u s e a n i n f o r m a l a p p r o a c h
Milliseconds 94 90 74 70 100 50 130 56 88 48 108 94 74 77 95 82 84 84 174 98 86 75 133 86 84
Character s o y o u w i l l s e e h o w t h e y
Milliseconds 76 51 109 64 132 82 72 59 58 113 186 61 81 80 517 148 97 96 61 70 57 65 128 51 118
Character l e a d n a t u r a l l y t o t h e m a i
Milliseconds 64 96 76 126 68 48 120 71 61 121 68 21 179 106 76 50 110 83 87 60 107 51 69 141 36
Character n i d e a o f t h i s h c a p t -h -a -p -t h
Milliseconds 85 76 92 73 150 75 76 87 98 87 82 48 87 54 64 151 0 157 66 100 568 0 0 0 100
Character a p t e r , t h e l i m i t . T h e i d e
Milliseconds 71 107 62 126 90 56 100 66 64 116 38 51 159 96 110 93 97 106 221 135 60 84 89 67 164
Character a o f a l i m i t p l a y s a f o u n
Milliseconds 60 91 77 120 122 34 165 32 164 93 130 90 51 98 92 91 93 120 53 115 61 63 45 94 173
Character d a i t o n a l -o -u -n -d -a -i -t -o -n -a -l - o u n d
Milliseconds 73 87 75 23 57 61 76 109 70 506 0 0 0 0 0 0 0 0 0 0 0 93 89 173 57
Character a t i o n a l r o l e t h r o u g h o u t c
Milliseconds 69 76 30 74 66 49 118 61 60 75 158 51 59 38 62 110 54 78 93 90 126 81 55 105 137
Character a l c u l u s .
Milliseconds 80 75 118 36 131 109 76 94
WPM Timing
Seconds WPM
1.69 99.59
3.37 117.37
5.06 94.85
6.75 104.92
8.43 112.39
10.12 117.37
11.81 120.93
13.5 120.04
15.18 120.93
16.87 122.35
18.56 122.87
20.24 122.11
21.93 116.55
23.62 117.37
25.3 119.03
26.99 119.15
28.68 119.25
30.37 120.14
32.05 121.3
33.74 122
35.43 122.62
37.11 123.52
38.8 124.02
40.49 124.78
42.17 125.2
43.86 125.03
45.55 125.41
47.23 122.96
48.92 123.63
50.61 124.25
52.3 124.6
53.98 124.71
55.67 124.81
57.36 124.49
59.04 124.38
60.73 124.49
62.42 124.77
64.1 124.86
65.79 125.31
67.48 125.55
69.16 125.61
70.85 125.16
72.54 125.39
74.23 125.78
75.91 124.56
77.6 124.33
79.29 124.41
80.97 122.56
82.66 122.82
84.35 122.92