(ginoo75)

Race #89413

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Official speed 168.83 wpm (61.41 seconds elapsed during race)
Without ending ping 169.39 wpm (203 ms delay sending score to TypeRacer’s server)
Timerless 169.40 wpm (3 ms elapsed before first character typed; 61.21 seconds elapsed during race)
Timerless minus one 169.20 wpm, ignoring the first character typed
Race Start April 25, 2024 3:27:02pm UTC
Race Finish April 25, 2024 3:28:04pm UTC
Outcome No win (1 of 1)
Accuracy 99.4%
Points 455.84
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 faa 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 pou red red into it? We see change occurring in nearly everything we observe in the world and univers,e ae, 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 stllope 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.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 3 67 41 98 90 69 168 134 76 28 67 96 71 70 41 37 118 130 47 64 29 69 55 20 43
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 103 76 27 107 46 71 103 57 63 34 35 77 90 61 92 61 27 85 54 49 29 36 69 69 76
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 35 48 37 96 61 42 37 41 33 90 58 60 15 65 61 415 112 62 100 94 79 55 75 36 96
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 65 56 32 50 103 48 57 82 56 76 13 106 50 96 20 70 28 99 40 64 10 65 21 82 35
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 48 35 63 56 82 49 56 86 67 127 33 63 54 84 56 34 44 74 23 40 62 76 70 77 132
Character d o f f a -a -f a f a l l i n g o b j e c t
Milliseconds 77 77 68 138 20 104 66 379 106 47 64 64 40 41 131 29 28 41 56 70 14 180 63 20 134
Character c h a n g e a s a f u n c t i o n o f
Milliseconds 26 99 34 41 83 49 49 36 62 41 82 56 92 41 54 127 48 153 12 36 22 147 55 82 67
Character t i m e ? H o w d o e s t h e l e v e l
Milliseconds 66 33 29 70 153 116 62 216 97 62 105 97 35 41 50 55 21 62 55 65 47 83 69 44 60
Character o f w a t e r i n a b a r r e l c h a n
Milliseconds 86 33 83 43 55 62 64 82 40 51 35 83 64 97 82 48 69 131 37 48 70 69 42 34 91
Character g e a s a f u n c t i o n o f t h e a
Milliseconds 42 40 42 68 57 78 60 91 15 75 161 57 144 64 42 19 139 48 56 90 42 16 67 64 84
Character m o u n t o f l i q u i d p o u r e d -r
Milliseconds 41 159 21 110 57 41 71 96 50 40 49 119 103 51 95 75 64 47 36 21 49 48 98 54 201
Character -e -d - - r e d i n t o i t ? W e s e e c
Milliseconds 0 0 0 537 41 64 82 35 35 41 84 42 91 68 90 160 132 208 160 91 55 56 130 71 82
Character h a n g e o c c u r r i n g i n n e a r l y
Milliseconds 55 79 56 42 41 41 50 61 132 78 82 132 96 21 42 61 58 28 82 57 49 84 74 34 65
Character e v e r y t h i n g w e o b s e r v e i n
Milliseconds 88 69 58 75 28 71 61 43 31 93 14 69 76 69 62 113 34 42 132 48 112 48 41 62 35
Character t h e w o r l d a n d u n i v e r s , e
Milliseconds 85 56 40 43 83 62 69 44 80 66 56 55 42 55 55 132 138 41 35 43 112 84 80 21 92
Character a -a - -e -, e , a n d p o w e r f u l m o d e
Milliseconds 42 249 120 131 126 33 142 129 118 68 57 48 57 26 43 132 40 127 84 40 119 54 56 33 84
Character r n i n s t r u m e n t s h e l p u s s e
Milliseconds 52 61 104 49 34 83 75 122 54 131 42 96 35 57 70 49 89 77 36 94 69 65 77 69 54
Character e m o r e a n d m o r e . I n t h i s
Milliseconds 140 68 65 33 42 28 49 64 61 50 39 71 34 55 21 56 105 110 140 97 55 48 29 58 37
Character s e c t i o n w e i n t r o d u c e t h e
Milliseconds 106 131 70 126 41 47 0 90 50 48 77 56 40 45 124 56 90 62 97 54 64 33 50 9 95
Character i d e a s o f a v e r a g e a n d i n s t
Milliseconds 43 41 76 47 134 63 76 71 68 56 91 56 62 61 69 35 61 57 44 49 53 78 26 51 62
Character a n t a n e o u s r a t e s o f c h a n g e
Milliseconds 89 64 90 76 63 165 84 33 56 86 47 85 67 49 111 83 21 117 44 83 57 144 83 78 36
Character , a n d s h o w t h a t t h e y a r e
Milliseconds 48 87 51 29 60 71 41 82 29 56 76 63 62 20 64 61 77 49 90 44 61 82 49 29 75
Character c l o s e l y r e l a t e d t o t h e s t
Milliseconds 64 82 134 7 31 79 55 84 27 49 63 83 36 61 76 63 81 10 98 53 29 28 88 44 61
Character l -l -t l o p e o f a c u r v e a t a p
Milliseconds 187 250 99 146 160 27 92 53 57 71 47 64 96 13 82 64 134 34 54 91 39 78 57 96 70
Character o i n t P o n t h e c u r v e . W e g
Milliseconds 27 125 35 42 49 99 130 85 56 68 62 26 56 38 61 105 61 139 49 55 63 69 90 90 90
Character i v e p r e c i s e d e v e l o p m e n t s
Milliseconds 92 48 57 43 80 50 33 139 110 71 37 82 47 50 130 43 63 145 14 167 104 78 76 54 49
Character o f t h e s e i m p o r t a n t c o n c e p
Milliseconds 85 54 77 50 26 22 111 34 61 45 35 109 14 49 130 72 8 88 56 98 63 41 49 60 71
Character t s i n t h e n e x t c h a p t e r , b
Milliseconds 76 91 89 92 26 70 30 59 23 74 64 42 146 64 67 258 62 97 82 58 90 70 28 105 74
Character u t f o r n o w w e u s e a n i n f o
Milliseconds 30 54 56 68 63 63 47 78 29 68 57 76 61 56 105 44 41 53 91 69 70 97 27 36 137
Character r m a l a p p r o a c h s o y o u w i l l
Milliseconds 56 66 143 84 104 47 71 112 41 84 61 58 68 69 50 82 76 257 99 12 57 34 84 56 96
Character s e e h o w t h e y l e a d n a t u r a
Milliseconds 55 50 55 124 43 90 14 49 62 62 56 71 60 35 27 70 69 71 65 46 48 70 90 47 42
Character l l y t o t h e m a i n i d e a o f t
Milliseconds 51 124 28 71 54 23 95 55 28 55 37 75 43 109 20 38 187 116 43 88 38 96 71 67 64
Character h i s c h a p t e r , t h e l i m i t . T
Milliseconds 19 23 42 82 57 119 74 84 75 58 69 33 92 47 14 84 55 20 50 97 49 96 113 47 84
Character h e i d e a o f a l i m i t p l a y s
Milliseconds 56 96 37 46 99 64 39 62 77 65 81 43 97 27 43 103 48 62 73 60 29 48 126 47 54
Character a f o u n d a t i o n a l r o l e t h r o u
Milliseconds 78 83 20 93 21 111 33 83 55 41 44 16 130 34 103 36 44 115 42 40 57 42 90 70 14
Character g h o u t c a l c u l u s .
Milliseconds 55 77 138 15 27 63 64 74 37 123 75 45 214 68 100
WPM Timing
Seconds WPM
1.23 156.32
2.46 175.86
3.68 185.63
4.91 170.98
6.14 175.86
7.37 180.75
8.6 178.66
9.83 170.98
11.05 172.61
12.28 171.96
13.51 170.54
14.74 172.61
15.97 173.61
17.2 173.77
18.42 172.61
19.65 165.48
20.88 162.65
22.11 162.84
23.34 165.58
24.56 166.09
25.79 166.56
27.02 160.32
28.25 161.42
29.48 161.62
30.71 163.36
31.93 163.46
33.16 164.65
34.39 165.4
35.62 165.42
36.85 165.44
38.07 166.72
39.3 167.93
40.53 165.21
41.76 165.52
42.99 165.82
44.22 165.55
45.44 165.3
46.67 166.35
47.9 166.34
49.13 166.34
50.36 166.81
51.59 166.56
52.81 166.55
54.04 167.43
55.27 167.61
56.5 168.43
57.73 168.59
58.95 168.94
60.18 169.68
61.41 168.83