Austin (austin_biceps)

Race #9419

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Official speed 122.99 wpm (84.30 seconds elapsed during race)
Without ending ping 123.31 wpm (221 ms delay sending score to TypeRacer’s server)
Timerless 123.81 wpm (335 ms elapsed before first character typed; 83.74 seconds elapsed during race)
Timerless minus one 123.66 wpm, ignoring the first character typed
Race Start January 10, 2024 3:59:50am UTC
Race Finish January 10, 2024 4:01:14am UTC
Outcome Win (1 of 3)
Accuracy 98.9%
Points 332.06
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 amoujnt nt of liquid poured into it? We see change occuinrrring in nearly everything we observe in the world iand universe, and powerful modern instruments help us see morea 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 slpoope of a curve a at a point P on the curve. We give precise developments of these important concepts in the next chapter, but for nowe we use an informal approach so you will see how they lead naturally to the ammain idea of this chapter, the milimit. 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 335 179 97 95 172 144 115 132 66 142 84 76 69 65 71 94 133 142 51 78 82 25 64 33 120
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 101 80 62 70 84 95 74 89 83 135 17 124 52 112 94 80 94 46 55 99 31 90 61 93 42
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 101 92 57 99 119 78 82 213 97 91 116 90 53 69 100 78 98 63 85 77 69 92 79 109 38
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 72 99 63 125 61 58 71 116 60 117 45 74 56 101 57 112 47 98 135 75 93 82 62 60 52
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 100 56 56 132 49 50 74 48 186 92 83 88 60 114 24 65 95 72 105 15 107 22 125 61 93
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 126 69 118 67 74 60 72 152 13 412 160 116 88 84 64 69 126 132 41 140 160 60 109 95 63
Character n g e a s a f u n c t i o n o f t i m e
Milliseconds 95 60 75 139 97 84 105 69 93 62 78 116 31 181 36 75 107 60 109 20 108 32 90 134 44
Character ? H o w d o e s t h e l e v e l o f w
Milliseconds 174 88 185 122 79 123 83 98 68 55 67 97 92 68 114 144 64 93 65 71 72 187 38 126 36
Character a t e r i n a b a r r e l c h a n g e a
Milliseconds 80 89 125 61 41 76 83 54 53 76 120 112 121 164 56 126 76 94 93 40 92 63 81 58 115
Character s a f u n c t i o n o f t h e a m o u j
Milliseconds 74 84 82 70 67 118 121 55 168 20 75 119 72 106 34 79 88 69 50 109 40 71 117 92 60
Character n t - -t -n -j n t o f l i q u i d p o u r e
Milliseconds 72 13 170 225 139 134 116 182 103 64 77 96 47 96 150 66 116 53 85 56 99 101 196 339 101
Character d i n t o i t ? W e s e e c h a n g e
Milliseconds 128 71 42 69 63 98 70 127 61 182 69 143 176 179 104 60 127 105 120 105 79 87 72 74 51
Character o c c u i n r -r -n -i r r i n g i n n e a r l y
Milliseconds 94 76 109 111 71 134 21 277 142 114 79 117 85 93 61 70 50 79 53 124 17 63 102 37 138
Character e v e r y t h i n g w e o b s e r v e i n
Milliseconds 74 70 80 118 53 80 101 75 57 88 50 75 73 54 68 50 122 80 131 44 166 69 67 61 71
Character t h e w o r l d i -i a n d u n i v e r s e
Milliseconds 60 11 137 24 94 68 105 92 261 136 92 111 332 80 93 38 79 118 145 34 63 126 58 125 67
Character , a n d p o w e r f u l m o d e r n i n s
Milliseconds 106 46 103 86 65 70 67 70 38 156 51 148 30 129 65 103 77 104 176 109 116 70 147 223 174
Character t r u m e n t s h e l p u s s e e m o r e
Milliseconds 144 121 71 154 73 100 74 43 75 136 57 121 61 71 148 70 83 105 73 154 49 90 66 62 59
Character a - -a a n d m o r e . I n t h i s s e
Milliseconds 175 99 208 119 53 102 89 79 72 74 67 34 73 95 54 177 124 69 82 77 40 74 48 107 45
Character c t i o n w e i n t r o d u c e t h e i d
Milliseconds 181 180 65 57 101 63 51 51 78 123 93 92 123 67 117 105 61 72 64 108 75 56 63 111 19
Character e a s o f a v e r a g e a n d i n s t a n
Milliseconds 126 82 135 104 123 80 86 61 117 149 69 111 121 89 332 173 94 72 62 87 84 29 126 65 95
Character t a n e o u s r a t e s o f c h a n g e ,
Milliseconds 82 187 116 140 121 88 104 57 90 64 124 59 64 59 100 59 54 124 79 40 102 101 83 70 38
Character a n d s h o w t h a t t h e y a r e c l
Milliseconds 74 93 39 98 73 89 66 80 69 106 107 68 64 77 75 81 61 81 67 32 84 74 34 117 61
Character o s e l y r e l a t e d t o t h e s l p o
Milliseconds 128 53 53 62 132 85 34 82 86 78 68 71 122 73 147 35 88 74 119 15 96 77 78 108 114
Character -o -p o p e o f a c u r v e a a -a - t a
Milliseconds 275 130 147 81 101 93 100 73 60 112 105 95 99 99 140 80 93 94 76 183 243 135 161 111 88
Character p o i n t P o n t h e c u r v e . W e
Milliseconds 67 139 115 416 181 84 87 199 96 67 138 101 60 105 40 69 71 91 73 136 83 74 45 159 160
Character g i v e p r e c i s e d e v e l o p m e n t
Milliseconds 89 91 87 87 67 52 97 61 70 133 82 107 61 82 98 138 118 86 72 150 60 127 65 85 73
Character s o f t h e s e i m p o r t a n t c o n c
Milliseconds 59 85 138 99 90 75 92 62 74 90 39 92 84 146 61 53 136 60 77 80 99 81 44 114 50
Character e p t s i n t h e n e x t c h a p t e r ,
Milliseconds 52 98 85 60 84 65 85 69 52 120 38 73 94 19 124 113 80 116 88 79 97 91 148 65 34
Character b u t f o r n o w e -e w e u s e a n
Milliseconds 73 142 38 83 85 107 72 102 38 87 61 103 77 291 130 374 69 114 159 93 62 93 110 45 80
Character i n f o r m a l a p p r o a c h s o y o u
Milliseconds 150 142 82 101 57 99 79 93 66 106 89 121 78 97 68 117 50 172 188 88 84 175 94 86 61
Character w i l l s e e h o w t h e y l e a d n a
Milliseconds 5 129 148 126 56 83 61 131 78 159 72 115 93 89 77 60 71 86 137 22 67 111 91 121 29
Character t u r a l l y t o t h e a m -m -a m a i n i
Milliseconds 90 128 75 34 71 138 153 81 132 55 75 65 134 58 72 92 86 308 120 124 118 59 77 64 138
Character d e a o f t h i s c h a p t e r , t h e
Milliseconds 42 134 51 64 114 52 64 101 69 81 31 94 69 110 27 156 107 160 59 59 51 104 64 66 66
Character m i -i -m l i m i t . T h e i d e a o f a
Milliseconds 63 91 329 127 112 158 127 58 82 98 40 153 110 74 74 106 85 141 50 62 119 67 65 51 92
Character l i m i t p l a y s a f o u n d a t i o n a
Milliseconds 97 158 141 75 61 107 196 100 113 202 123 82 71 64 99 74 85 124 42 84 127 64 55 102 93
Character l r o l e t h r o u g h o u t c a l c u l u
Milliseconds 60 60 93 106 122 51 62 118 69 85 61 62 90 78 115 68 62 58 117 65 113 95 109 169 155
Character s .
Milliseconds 85 81
WPM Timing
Seconds WPM
1.69 85.41
3.37 117.44
5.06 128.11
6.74 129.89
8.43 132.39
10.12 136.42
11.8 136.25
13.49 132.56
15.17 132.86
16.86 133.1
18.55 133.29
20.23 133.45
21.92 134.68
23.6 129.13
25.29 127.17
26.98 126.78
28.66 123.93
30.35 124.95
32.03 126.62
33.72 124.91
35.41 125.4
37.09 124.56
38.78 124.71
40.46 123.96
42.15 124.41
43.84 125.1
45.52 123.9
47.21 124.05
48.89 125.17
50.58 126.22
52.27 126.97
53.95 125.45
55.64 123.8
57.32 122.88
59.01 123.23
60.7 123.37
62.38 123.88
64.07 124.56
65.75 124.83
67.44 123.67
69.13 123.77
70.81 123.54
72.5 124.14
74.18 123.1
75.87 123.69
77.56 122.7
79.24 123.12
80.93 122.78
82.61 123.18
84.3 122.99