Cepheus's 🌌 (parkevan27)

Race #88663

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Official speed 163.11 wpm (63.56 seconds elapsed during race)
Without ending ping 163.62 wpm (197 ms delay sending score to TypeRacer’s server)
Timerless 164.52 wpm (348 ms elapsed before first character typed; 63.02 seconds elapsed during race)
Timerless minus one 164.33 wpm, ignoring the first character typed
Race Start May 2, 2024 5:47:09am UTC
Race Finish May 2, 2024 5:48:12am UTC
Outcome Win (1 of 3)
Accuracy 99.3%
Points 440.40
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 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 th se slope of a curve at a point P on the curve. We give precise developments of these important concepts in the next chpaapter, but for now ewe use an informal approach so you will see how they lead naturally to the main idea of this chapter, the limit. The iede oa of a limit plays a foundational role throughout acalculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 348 120 297 109 80 97 67 98 57 44 70 64 67 49 74 41 109 111 64 67 67 68 23 26 85
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 65 79 36 65 68 67 89 66 101 30 56 127 41 100 46 83 34 78 47 92 31 55 50 93 47
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 69 40 116 0 75 32 53 83 39 64 83 46 70 51 71 79 54 82 103 42 130 54 17 54 86
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 76 36 44 70 54 42 52 100 92 67 60 40 58 98 56 60 92 36 59 57 50 130 26 50 72
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 56 46 63 22 74 78 21 24 161 75 103 65 78 66 66 69 48 84 48 84 32 86 34 105 117
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 132 13 45 169 100 76 92 81 48 104 119 172 38 78 40 70 82 70 93 117 135 34 223 97 79
Character n g e a s a f u n c t i o n o f t i m e
Milliseconds 77 26 50 90 10 171 77 57 109 18 130 122 71 101 61 115 32 49 77 33 79 50 77 23 64
Character ? H o w d o e s t h e l e v e l o f w
Milliseconds 166 54 209 102 81 71 50 71 71 75 34 66 83 55 46 29 229 107 55 43 53 84 41 92 50
Character a t e r i n a b a r r e l c h a n g e a
Milliseconds 41 43 97 50 55 83 35 80 37 62 68 130 22 152 75 67 37 33 72 91 51 24 62 39 175
Character s a f u n c t i o n o f t h e a m o u n
Milliseconds 102 67 81 72 44 116 123 84 126 57 121 25 50 68 54 50 68 81 53 75 70 53 82 64 129
Character t o f l i q u i d p o u r e d i n t o i
Milliseconds 49 71 38 81 56 60 45 120 76 45 82 82 140 143 47 39 51 97 40 101 36 72 29 66 87
Character t ? W e s e e c h a n g e o c c u r r i n
Milliseconds 37 160 27 168 77 71 81 131 116 70 58 83 88 45 70 44 32 29 87 126 57 96 132 92 26
Character g i n n e a r l y e v e r y t h i n g w e
Milliseconds 67 87 75 38 47 84 66 43 27 74 24 36 29 123 98 54 27 99 39 38 63 110 61 74 115
Character o b s e r v e i n t h e w o r l d a n d
Milliseconds 46 49 83 96 101 35 125 82 65 76 41 46 40 70 44 68 40 46 80 47 91 66 79 49 74
Character u n i v e r s e , a n d p o w e r f u l m
Milliseconds 41 68 107 57 23 89 49 91 88 64 31 71 70 54 56 52 51 55 78 68 95 28 20 84 91
Character o d e r n i n s t r u m e n t s h e l p u s
Milliseconds 27 54 89 44 60 25 84 33 50 71 60 64 152 101 51 71 80 34 94 59 68 43 29 92 56
Character s e e m o r e a n d m o r e . I n t h
Milliseconds 103 34 121 121 61 118 31 38 45 31 95 35 85 28 108 18 65 26 62 54 117 112 52 74 58
Character i s s e c t i o n w e i n t r o d u c e t
Milliseconds 29 119 28 53 101 131 124 70 107 20 49 47 83 48 84 37 46 120 71 75 88 64 93 65 102
Character h e i d e a s o f a v e r a g e a n d i
Milliseconds 79 63 65 34 50 118 53 80 65 22 66 81 133 104 111 60 71 65 37 76 75 88 80 67 73
Character n s t a n t a n e o u s r a t e s o f c h a
Milliseconds 30 96 65 77 55 46 95 96 82 90 72 47 85 66 57 69 19 101 14 31 157 127 66 79 71
Character n g e , a n d s h o w t h a t t h e y a
Milliseconds 73 17 24 158 59 93 78 65 66 69 70 41 34 97 55 80 52 36 83 40 88 29 84 33 56
Character r e c l o s e l y r e l a t e d t o t h
Milliseconds 42 69 19 70 60 40 64 76 61 0 73 25 41 62 73 42 40 108 99 65 64 17 73 67 107
Character s -s - e s l o p e o f a c u r v e a t
Milliseconds 73 233 106 75 65 73 29 55 111 111 100 0 57 75 68 66 67 102 52 127 56 63 67 65 52
Character a p o i n t P o n t h e c u r v e . W
Milliseconds 50 88 74 159 19 39 59 70 158 103 97 32 43 47 75 34 55 61 71 61 123 62 77 100 26
Character e g i v e p r e c i s e d e v e l o p m e n
Milliseconds 88 61 83 78 51 38 52 63 86 35 114 104 45 97 65 71 136 94 55 51 116 61 167 79 81
Character t s o f t h e s e i m p o r t a n t c o n
Milliseconds 45 81 67 49 83 53 72 61 51 101 111 68 108 51 71 91 76 113 74 57 41 78 57 65 18
Character c e p t s i n t h e n e x t c h p a -a -p a
Milliseconds 72 147 23 109 83 54 93 38 46 30 78 62 84 48 68 140 113 86 52 92 230 14 273 116 85
Character p t e r , b u t f o r n o w e -e w e u s
Milliseconds 60 80 77 71 30 41 71 59 73 45 75 25 96 46 78 22 51 36 91 299 64 83 20 76 34
Character e a n i n f o r m a l a p p r o a c h s o
Milliseconds 103 45 85 53 58 60 39 73 45 85 47 97 68 42 67 93 102 133 31 192 126 87 24 48 76
Character y o u w i l l s e e h o w t h e y l e
Milliseconds 54 113 38 42 32 31 108 115 100 73 14 128 118 100 72 30 34 73 50 56 61 58 33 54 25
Character a d n a t u r a l l y t o t h e m a i n
Milliseconds 51 87 51 66 64 46 68 63 63 34 100 42 49 71 46 54 36 82 34 57 96 112 25 75 17
Character i d e a o f t h i s c h a p t e r , t h e
Milliseconds 57 53 121 36 90 39 53 84 51 80 23 43 58 60 57 75 50 71 93 68 21 35 61 67 65
Character l i m i t . T h e i e -e d e o -o - a o f
Milliseconds 21 45 61 116 29 81 87 16 77 108 35 79 65 156 220 163 266 198 11 344 109 71 47 70 44
Character a l i m i t p l a y s a f o u n d a t i
Milliseconds 69 84 65 17 58 183 28 128 57 61 102 85 56 101 55 77 315 0 0 0 30 85 0 49 41
Character o n a l r o l e t h r o u g h o u t a -a c a
Milliseconds 72 0 85 54 79 75 48 92 85 51 43 64 72 51 23 92 56 61 65 28 99 80 244 200 57
Character l c u l u s .
Milliseconds 92 88 67 75 49 92 20
WPM Timing
Seconds WPM
1.27 75.51
2.54 132.15
3.81 151.03
5.09 160.47
6.36 166.13
7.63 169.91
8.9 168.56
10.17 165.19
11.44 162.56
12.71 161.41
13.98 160.47
15.26 161.25
16.53 162.65
17.8 161.82
19.07 162.35
20.34 162.83
21.61 161.58
22.88 162.56
24.15 163.45
25.43 164.24
26.7 165.41
27.97 166.47
29.24 166.62
30.51 167.55
31.78 167.64
33.05 167.73
34.32 167.46
35.6 167.21
36.87 167.63
38.14 169.59
39.41 167.47
40.68 167.55
41.95 167.62
43.22 167.96
44.5 167.21
45.77 167.02
47.04 167.36
48.31 165.43
49.58 165.55
50.85 164.95
52.12 164.38
53.39 164.51
54.67 165.74
55.94 166.47
57.21 167.39
58.48 165.19
59.75 163.68
61.02 164.01
62.29 164.51
63.56 163.11