lufle (lufle)

Race #593

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Official speed 139.09 wpm (74.54 seconds elapsed during race)
Without ending ping 139.41 wpm (170 ms delay sending score to TypeRacer’s server)
Timerless 140.64 wpm (653 ms elapsed before first character typed; 73.72 seconds elapsed during race)
Timerless minus one 140.48 wpm, ignoring the first character typed
Race Start February 1, 2025 9:44:09am UTC
Race Finish February 1, 2025 9:45:23am UTC
Outcome Win (1 of 3)
Opponents 2. _ehsaas_gupta (135.91 wpm)
Accuracy 98.8%
Points 375.53
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 squantity 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 maamount of liquid poured into it? We see change occurring in nearly aeeverything 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 instenaanteaaneous 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 nwo we now we use an informal approach so you will see how they lead naturally to hte the main idea of thi scs 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 653 168 97 74 102 47 188 208 51 84 149 49 119 89 113 68 100 111 44 95 81 41 55 28 123
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 49 24 53 427 50 140 108 31 151 140 42 68 66 93 80 77 101 64 53 84 40 0 78 105 69
Character c h a n g e i n o n e s -s q u a n t i t y
Milliseconds 145 38 80 53 91 55 53 42 32 71 96 43 60 53 111 256 78 58 92 76 89 68 100 83 25
Character i s r e l a t e d t o a c h a n g e i n
Milliseconds 70 171 53 125 72 51 89 143 41 118 34 127 14 84 125 85 210 66 102 62 100 58 41 60 28
Character a n o t h e r . H o w d o e s t h e s p
Milliseconds 63 117 76 47 19 63 81 64 40 92 111 124 93 64 140 79 55 49 69 99 43 67 57 119 47
Character e e d o f a f a l l i n g o b j e c t c
Milliseconds 103 115 135 98 67 55 62 89 63 143 79 82 131 64 55 46 52 77 45 84 75 99 168 55 147
Character h a n g e a s a f u n c t i o n o f t i
Milliseconds 30 74 75 57 35 60 114 84 44 122 62 97 59 125 52 154 21 64 142 24 72 119 0 82 51
Character m e ? H o w d o e s t h e l e v e l o f
Milliseconds 95 105 379 0 0 98 39 35 160 34 89 37 47 122 41 88 29 67 102 51 81 48 85 72 59
Character w a t e r i n a b a r r e l c h a n g e
Milliseconds 40 108 48 126 60 52 58 43 48 86 97 37 70 149 167 114 35 66 76 118 39 77 65 71 52
Character a s a f u n c t i o n o f t h e m a -a
Milliseconds 64 150 130 54 82 73 85 57 108 63 147 18 70 92 51 67 49 54 89 32 95 40 80 36 350
Character -m a m o u n t o f l i q u i d p o u r e d
Milliseconds 108 89 53 130 52 136 23 42 76 88 45 85 37 149 120 53 107 48 68 55 68 65 61 158 51
Character i n t o i t ? W e s e e c h a n g e o c
Milliseconds 130 47 90 79 62 152 70 164 98 152 149 33 240 93 118 36 146 60 48 84 72 35 40 34 102
Character c u r r i n g i n n e a r l y a e -e -a e v e
Milliseconds 109 86 89 127 76 44 86 34 73 36 55 97 38 65 68 94 65 48 90 167 129 119 56 85 138
Character r y t h i n g w e o b s e r v e i n t h e
Milliseconds 83 29 160 34 126 43 53 66 122 38 51 128 87 129 53 48 173 66 64 82 40 34 95 69 34
Character w o r l d a n d u n i v e r s e , a n d
Milliseconds 18 114 84 81 50 97 53 113 85 99 68 98 54 121 47 68 54 79 64 333 47 99 77 61 47
Character p o w e r f u l m o d e r n i n s t r u m e n
Milliseconds 88 46 65 54 65 134 45 31 95 79 53 66 96 41 42 89 34 50 65 96 33 58 157 68 94
Character t s h e l p u s s e e m o r e a n d m
Milliseconds 56 54 72 93 41 58 33 72 94 53 67 132 58 132 100 33 42 89 29 66 108 78 72 59 117
Character o r e . I n t h i s s e c t i o n w e i
Milliseconds 31 73 44 84 77 146 161 56 115 63 81 101 54 139 43 164 150 69 56 113 31 99 50 49 99
Character n t r o d u c e t h e i d e a s o f a v e
Milliseconds 50 67 50 53 107 66 92 98 34 117 54 89 43 51 54 115 81 117 29 70 67 123 61 164 103
Character r a g e a n d i n s t e n -n a -a -e a n t e a -a
Milliseconds 56 109 70 54 51 133 106 74 44 104 29 157 175 87 136 211 137 232 117 72 85 42 68 114 218
Character -e a n e o u s r a t e s o f c h a n g e ,
Milliseconds 113 85 82 76 83 42 72 38 122 50 122 55 149 77 66 84 19 149 33 97 43 232 61 69 33
Character a n d s h o w t h a t t h e y a r e c l
Milliseconds 61 117 55 31 120 81 48 55 74 156 67 103 52 52 113 64 63 68 51 150 31 68 41 140 59
Character o s e l y r e l a t e d t o t h e s l o p
Milliseconds 113 48 53 43 94 114 248 0 0 111 33 68 129 46 87 74 119 52 46 82 55 115 31 142 42
Character e o f a c u r v e a t a p o i n t P
Milliseconds 75 39 52 82 36 51 89 126 90 52 142 67 49 124 75 57 201 74 147 38 42 140 71 31 98
Character o n t h e c u r v e . W e g i v e p r
Milliseconds 98 116 41 37 123 22 99 21 151 63 94 145 33 33 123 142 158 57 110 84 103 31 49 69 81
Character e c i s e d e v e l o p m e n t s o f t h e
Milliseconds 49 155 88 52 56 66 169 30 124 77 18 123 46 138 42 102 35 37 33 98 100 49 112 52 59
Character s e i m p o r t a n t c o n c e p t s i n
Milliseconds 73 77 44 73 123 122 53 50 59 66 69 66 51 146 42 34 81 92 77 75 49 75 50 29 63
Character t h e n e x t c h a p t e r , b u t f o r
Milliseconds 125 41 85 50 52 120 270 108 55 128 68 48 74 80 46 37 47 54 68 114 56 60 96 76 59
Character n w o w e -w -e - -n -w -o - n o w w e u s e
Milliseconds 42 85 29 26 57 104 59 49 301 0 0 132 0 0 0 282 34 72 45 133 100 5 144 56 69
Character a n i n f o r m a l a p p r o a c h s o
Milliseconds 49 128 70 80 49 53 64 83 68 74 42 83 21 105 97 127 64 96 71 45 75 75 57 83 44
Character y o u w i l l s e e h o w t h e y l e a
Milliseconds 106 66 36 19 113 76 47 94 66 100 50 122 62 105 48 64 39 127 66 67 82 54 272 91 74
Character d n a t u r a l l y t o h t e -h -t -e - t h
Milliseconds 144 84 78 40 58 107 68 39 68 109 40 47 138 56 79 96 16 130 53 371 0 0 0 192 67
Character e m a i n i d e a o f t h i s c -c -s - s
Milliseconds 58 63 27 117 67 48 58 99 29 132 53 49 30 65 85 340 78 9 223 20 238 213 127 113 64
Character c h a p t e r , t h e l i m i t . T h e
Milliseconds 33 118 22 105 72 142 39 78 34 54 195 64 76 58 26 42 121 120 44 123 111 125 119 66 40
Character i d e a o f a l i m i t p l a y s a f
Milliseconds 104 37 156 21 66 65 58 57 91 67 52 41 106 104 33 47 95 50 26 56 118 66 401 33 132
Character o u n d a t i o n a l r o l e t h r o u g h o
Milliseconds 68 32 126 47 113 47 33 40 130 64 52 65 87 55 109 51 21 142 43 84 60 35 98 51 17
Character u t c a l c u l u s .
Milliseconds 51 54 63 172 30 32 127 59 58 106 65 81
WPM Timing
Seconds WPM
1.49 56.34
2.98 100.61
4.47 107.32
5.96 124.76
7.45 122.35
8.95 124.76
10.44 129.94
11.93 132.81
13.42 134.15
14.91 136.03
16.4 137.57
17.89 140.86
19.38 140.55
20.87 140.86
22.36 138.98
23.85 138.85
25.34 138.73
26.84 139.52
28.33 138.11
29.82 138.85
31.31 138.75
32.8 140.49
34.29 141.39
35.78 141.87
37.27 141.99
38.76 142.72
40.25 142.2
41.74 138.27
43.23 137.95
44.73 138.18
46.22 138.91
47.71 139.35
49.2 139.52
50.69 139.91
52.18 139.83
53.67 140.41
55.16 140.97
56.65 141.07
58.14 140.55
59.63 139.65
61.12 140.37
62.62 140.86
64.11 140.95
65.6 139.4
67.09 138.8
68.58 137.71
70.07 138.03
71.56 138.18
73.05 138.64
74.54 139.09