Owen (owenxc1234)

Race #3389

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Official speed 121.62 wpm (85.25 seconds elapsed during race)
Without ending ping 121.97 wpm (245 ms delay sending score to TypeRacer’s server)
Timerless 122.20 wpm (158 ms elapsed before first character typed; 84.85 seconds elapsed during race)
Timerless minus one 122.06 wpm, ignoring the first character typed
Race Start November 8, 2023 8:04:32pm UTC
Race Finish November 8, 2023 8:05:57pm UTC
Outcome Win (1 of 5)
Accuracy 98.2%
Points 328.38
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 leve of el of water in a barrel change as a function of the amount of liquid poiureured into it? We see chang eocce ocucuring in ring in nearly everything we obnserve in the world an dunid universe, and powerful modern instruments help us see more and more. In this secrtion we introruorduce the ideas of average and instatnntaneous rates of ahchange, and show that they are closely related to the slope of a curve at a point P on the dcurve. 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 maiun in idea of this chapter, the limit. The ideas of of a limit plays a foundational role throhughout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 158 180 124 9 491 97 80 65 94 58 101 63 64 75 62 76 142 188 66 90 57 35 73 9 53
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 109 58 59 79 57 112 149 70 77 106 381 69 106 95 103 102 43 110 41 68 52 61 33 98 81
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 93 89 66 72 117 54 28 79 52 60 93 64 78 57 111 79 101 96 126 105 89 117 25 129 53
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 47 113 41 90 17 141 88 67 39 125 17 73 83 72 93 80 76 67 99 53 22 54 55 70 49
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 80 56 52 104 27 54 131 65 139 131 31 82 81 120 106 44 77 95 79 60 73 69 105 78 130
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 62 30 56 102 54 58 103 68 63 48 114 57 65 54 20 76 172 187 60 43 177 66 77 53 88
Character n g e a s a f u n c t i o n o f t i m e
Milliseconds 39 113 47 56 73 70 67 99 77 86 108 56 0 160 40 61 0 70 99 62 38 100 53 43 68
Character ? H o w d o e s t h e l e v e o f - -f
Milliseconds 155 70 126 131 63 67 96 99 82 35 75 81 77 36 109 57 40 111 68 408 36 111 56 318 105
Character -o - -e e l o f w a t e r i n a b a r r e
Milliseconds 120 128 145 343 91 76 104 107 7 104 45 110 92 49 17 83 62 70 89 41 58 69 81 147 60
Character l c h a n g e a s a f u n c t i o n o f
Milliseconds 143 85 79 78 59 79 85 52 63 84 60 63 81 68 88 96 47 22 174 11 54 0 87 88 72
Character t h e a m o u n t o f l i q u i d p o i
Milliseconds 40 117 67 79 81 62 67 57 119 14 89 39 64 93 60 54 47 98 136 96 86 85 62 60 176
Character u r e -e -r -u -i u r e d i n t o i t ? W e s
Milliseconds 61 23 117 217 84 120 119 148 16 83 57 47 68 45 118 40 97 128 82 182 55 96 165 95 236
Character e e c h a n g e o c c -c -c -o -e - e o c u -u c
Milliseconds 154 128 66 80 74 65 73 98 45 0 69 99 130 232 112 131 123 114 109 12 71 76 204 303 118
Character u r i n g i n - -n -i - -g -n -i r i n g i n n
Milliseconds 91 74 86 38 74 45 61 48 81 362 136 120 132 130 123 133 106 38 74 82 0 109 86 82 138
Character e a r l y e v e r y t h i n g w e o b n -n s
Milliseconds 78 63 52 84 139 68 81 152 59 91 45 98 66 64 54 54 82 86 38 79 26 225 0 424 122
Character e r v e i n t h e w o r l d a n d u n i
Milliseconds 47 81 203 90 60 68 65 218 143 78 64 39 106 17 155 12 161 30 117 33 128 0 143 72 100
Character -i -n -u -d - d u n i v e r s e , a n d p o w e
Milliseconds 234 118 113 132 123 65 41 112 56 97 82 133 62 92 88 90 65 66 119 75 96 64 90 76 39
Character r f u l m o d e r n i n s t r u m e n t s h
Milliseconds 34 147 43 84 23 134 64 56 108 63 82 24 103 69 58 124 133 100 144 99 54 66 66 63 50
Character e l p u s s e e m o r e a n d m o r e .
Milliseconds 86 84 53 87 180 86 67 127 76 129 75 77 81 51 78 146 90 81 63 35 81 34 63 46 114
Character I n t h i s s e c r -r t i o n w e i n t
Milliseconds 64 138 147 64 61 79 59 29 80 203 81 76 176 454 71 107 38 25 67 86 47 76 71 54 65
Character r o r u -u -r -o o r -r d u c e t h e i d e a s
Milliseconds 125 67 89 97 383 116 123 560 124 319 72 89 51 75 90 102 73 29 67 104 75 72 44 106 65
Character o f a v e r a g e a n d i n s t a t n -n -t n
Milliseconds 44 99 56 75 133 139 46 104 106 58 61 76 91 94 86 139 80 111 148 56 174 0 365 90 180
Character t a n e o u s r a t e s o f a h -h -a c h a n
Milliseconds 76 67 195 117 102 42 80 69 95 46 143 61 61 67 39 87 63 93 95 385 97 96 58 42 90
Character g e , a n d s h o w t h a t t h e y a r
Milliseconds 71 49 78 48 63 106 0 134 64 142 33 65 60 92 86 27 79 34 125 66 80 59 43 66 41
Character e c l o s e l y r e l a t e d t o t h e
Milliseconds 54 45 148 105 237 76 49 84 101 63 87 51 81 64 85 111 38 51 119 53 44 99 91 40 87
Character s l o p e o f a c u r v e a t a p o i
Milliseconds 74 39 166 83 11 22 100 254 105 103 83 130 100 102 130 68 45 97 92 59 89 76 63 49 170
Character n t P o n t h e d -d c u r v e . W e g
Milliseconds 52 30 65 120 145 53 71 73 63 88 71 36 124 290 127 87 116 178 67 73 69 164 190 58 109
Character i v e p r e c i s e d e v e l o p m e n t s
Milliseconds 77 109 34 39 86 227 60 127 103 87 80 46 130 71 126 61 54 147 33 118 98 69 282 66 119
Character o f t h e s e i m p o r t a n t c o n c e p
Milliseconds 58 98 38 114 56 86 91 41 27 112 96 92 62 44 136 62 72 70 82 79 108 55 71 77 72
Character t s i n t h e n e x t c h a p t e r , b
Milliseconds 128 164 93 62 63 74 49 87 69 69 66 42 23 96 48 96 87 21 124 63 109 47 28 47 136
Character u t f o r n o w w e u s e a n i n f o
Milliseconds 40 50 51 103 31 102 7 87 45 56 79 85 36 78 151 112 47 46 95 93 26 103 67 103 31
Character r m a l a p p r o a c h s o y o u w i l l
Milliseconds 155 37 106 413 115 123 79 112 73 99 87 124 174 91 178 53 43 119 18 54 38 74 82 144 100
Character s e e h o w t h e y l e a d n a t u r a
Milliseconds 64 27 59 105 64 146 93 8 66 93 67 61 72 47 159 94 121 101 0 95 120 183 123 66 46
Character l l y t o t h e m a i u n i -i - -n -u n i
Milliseconds 92 106 45 68 94 56 51 70 73 57 110 32 87 82 0 15 81 129 244 104 129 125 228 84 90
Character d e a o f t h i s c h a p t e r , t h e
Milliseconds 63 76 126 74 49 78 79 68 57 33 39 54 84 81 56 80 70 104 44 13 47 96 73 28 56
Character l i m i t . T h e i d e a s o f - -f -o - -s
Milliseconds 86 93 55 153 123 125 65 196 186 76 80 54 47 77 56 101 58 62 88 51 269 103 125 135 121
Character o f a l i m i t p l a y s a f o u n d
Milliseconds 95 67 49 69 66 102 40 72 64 129 92 58 27 75 90 104 96 40 98 63 79 87 44 54 20
Character a t i o n a l r o l e t h r o h -h u g h o u t
Milliseconds 112 144 46 15 36 123 74 68 80 81 138 76 40 123 35 108 45 201 475 171 52 68 70 52 119
Character c a l c u l u s .
Milliseconds 0 100 83 0 132 70 90 108 89 107
WPM Timing
Seconds WPM
1.7 98.53
3.41 123.17
5.11 124.34
6.82 130.21
8.52 137.95
10.23 140.76
11.93 142.77
13.64 143.4
15.34 145.46
17.05 135.84
18.75 133.73
20.46 134.9
22.16 138.6
23.87 133.22
25.57 132.32
27.28 127.57
28.98 122.96
30.69 120.04
32.39 121.5
34.1 120
35.8 116.97
37.51 118.05
39.21 119.04
40.92 119.94
42.62 121.06
44.33 119.92
46.03 115.74
47.74 117.14
49.44 116.25
51.15 116.6
52.85 116.02
54.56 117.23
56.26 118.8
57.97 118.82
59.67 118.64
61.38 118.48
63.08 118.51
64.79 119.46
66.49 120.37
68.2 121.76
69.9 121.54
71.61 122
73.31 122.1
75.02 122.05
76.72 122.15
78.43 122.4
80.13 121.15
81.84 122
83.54 121.8
85.25 121.62