retired (yourally_)

Race #1727

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Official speed 118.99 wpm (87.13 seconds elapsed during race)
Without ending ping 119.24 wpm (184 ms delay sending score to TypeRacer’s server)
Timerless 119.99 wpm (543 ms elapsed before first character typed; 86.41 seconds elapsed during race)
Timerless minus one 119.85 wpm, ignoring the first character typed
Race Start December 25, 2023 10:28:24pm UTC
Race Finish December 25, 2023 10:29:51pm UTC
Outcome Win (1 of 4)
Accuracy 96.6%
Points 321.26
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 relate d to a change in anohter,ther. How does the speed foof a falling object change the fuas a function of time? hHow does the lvel olevel of water ina ba a barrel change as the a f uunction asof the amount of liquid poured into it?W We see change occuring in ring in nearly everytihing we observe in the world and univrerse, and powerful modern instruments help use see more and more. In this section we introduce the ideas of average and instatennteaneous rates of ahchange, and show that they are closely related to the slpoope of a curve at a point P on the curve. We tive give prescise cdevelpoopments of these important cconcepts in the next chapter, but for now we use an informal papproach cso you will see how they lead naturally to the main idea of this schapter, 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 543 143 131 85 102 128 101 122 40 154 63 50 109 48 110 52 120 73 63 137 21 34 87 52 18
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 125 50 53 91 0 122 108 61 128 103 31 133 390 174 27 157 171 50 122 25 75 42 77 95 47
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 119 45 95 39 100 20 61 55 65 59 76 63 70 53 129 76 71 116 94 68 84 103 54 69 109
Character r e l a t e - d t o a c h a n g e i n
Milliseconds 41 74 37 78 91 46 38 86 316 98 51 145 134 114 102 46 85 107 48 56 75 29 84 54 50
Character a n o h t e r , -, -r -e -t -h t h e r . H o w d
Milliseconds 64 96 53 54 106 0 152 22 113 221 112 149 112 137 93 39 105 33 93 86 191 171 144 91 93
Character o e s t h e s p e e d f o -o -f o f a f a
Milliseconds 66 48 13 91 74 77 40 138 59 90 71 107 72 85 95 122 212 96 73 72 77 63 82 64 49
Character l l i n g o b j e c t c h a n g e t h e f
Milliseconds 50 133 39 78 44 24 80 79 67 70 95 103 50 145 32 188 65 111 26 64 80 43 73 85 73
Character u -f -u -t -h -e - a s a f u n c t i o n o f t
Milliseconds 91 246 0 108 0 0 0 164 181 188 63 101 56 75 103 40 131 47 0 44 64 40 116 56 55
Character i m e ? h -h H o w d o e s t h e l v e l
Milliseconds 46 64 47 180 75 385 213 223 145 112 72 51 86 50 17 85 94 38 109 72 24 150 40 37 92
Character o -o -l -v -e -l - l e v e l o f w a t e r i n a
Milliseconds 56 257 99 0 0 0 0 179 98 77 64 78 86 70 45 195 0 87 30 97 51 59 56 70 213
Character b a -a -b - -a a b a r r e l c h a n g e a
Milliseconds 92 116 64 200 121 153 114 53 185 141 127 89 101 163 45 93 76 141 47 83 37 79 36 77 63
Character s t h e - -t -h -e a f u -u - u n c t i o n
Milliseconds 18 111 66 55 61 92 246 96 0 0 245 50 178 0 273 186 100 168 98 55 110 38 34 37 60
Character a s -s -a o f t h e a m o u n t o f l i q u
Milliseconds 123 20 162 117 83 138 0 92 76 49 67 87 65 55 77 155 0 68 65 82 84 53 43 120 66
Character i d p o u r e d i n t o i t ? W -W W e s
Milliseconds 71 69 81 37 38 135 57 39 63 33 52 64 109 43 64 85 50 200 126 359 140 63 167 103 49
Character e e c h a n g e o c c u r i n g i n - -n -i
Milliseconds 40 114 51 117 32 65 56 44 50 63 30 187 135 66 139 21 39 72 36 58 57 43 203 144 125
Character - -g -n -i r i n g i n n e a r l y e v e r y t
Milliseconds 155 133 119 125 54 125 58 83 97 94 44 61 251 90 15 19 119 70 66 83 91 98 33 109 38
Character i -i h i n g w e o b s e r v e i n t h e
Milliseconds 259 441 99 83 54 76 40 130 18 49 104 87 127 24 38 136 26 61 65 38 68 11 98 49 119
Character w o r l d a n d u n i v r -r e r s e , a n d
Milliseconds 66 63 55 119 50 104 41 113 62 11 116 145 57 118 136 478 54 35 147 0 63 61 79 132 60
Character p o w e r f u l m o d e r n i n s t r u m e
Milliseconds 84 51 17 83 18 35 96 64 86 73 112 18 56 111 32 64 36 99 23 32 60 54 53 154 90
Character n t s h e l p u s e -e s e e m o r e a n
Milliseconds 72 83 25 61 32 97 35 94 19 67 102 37 387 109 77 36 107 72 50 56 33 22 81 73 51
Character d m o r e . I n t h i s s e c t i o n w
Milliseconds 70 52 55 39 49 20 135 0 171 224 62 124 38 62 52 126 385 91 167 107 46 92 0 115 93
Character e i n t r o d u c e t h e i d e a s o f
Milliseconds 16 136 120 229 95 72 96 86 96 53 128 36 85 44 83 66 34 52 131 27 387 232 65 2342 85
Character a v e r a g e a n d i n s t a t e n -n -e -t n t
Milliseconds 125 215 57 63 117 43 33 87 133 20 104 32 81 40 85 48 61 161 79 157 172 133 118 115 99
Character e -e a n e o u s r a t e s o f a h -h -a c h a
Milliseconds 135 369 122 79 111 116 42 76 90 62 97 47 22 66 9 74 72 65 146 45 210 97 42 105 41
Character n g e , a n d s h o w t h a t t h e y a
Milliseconds 86 63 32 113 64 75 94 58 80 310 148 56 30 82 65 76 57 50 70 84 58 62 84 36 41
Character r e c l o s e l y r e l a t e d t o t h e
Milliseconds 86 0 47 92 56 109 65 20 77 68 86 117 66 157 0 56 19 71 27 107 48 35 100 50 79
Character s l p o -o -p o p e o f a c u r v e a t
Milliseconds 73 44 110 101 0 389 116 143 76 52 60 57 69 82 48 93 71 116 75 133 33 116 270 42 66
Character a p o i n t P o n t h e c u r v e . W
Milliseconds 90 76 68 17 80 16 69 44 210 114 125 67 60 57 79 58 65 87 72 64 122 22 220 75 109
Character e t i v e -t -i -v -e - g i v e p r e s -s c i s
Milliseconds 162 98 75 114 47 41 76 242 0 0 0 0 210 58 55 24 111 15 58 50 120 212 102 122 59
Character e c -c d e v e l p o -o -p o p m e n t s o f t
Milliseconds 28 70 230 331 87 128 89 54 79 151 32 368 166 159 100 72 96 66 86 36 55 50 101 62 118
Character h e s e i m p o r t a n t c -c c o n c e p t s
Milliseconds 48 59 147 26 50 382 149 126 22 107 115 40 65 129 73 84 262 194 107 38 41 108 77 95 80
Character i n t h e n e x t c h a p t e r , b u t
Milliseconds 49 68 50 60 47 78 57 77 20 67 126 104 122 77 89 61 90 84 101 50 40 46 97 41 77
Character f o r n o w w e u s e a n i n f o r m
Milliseconds 54 69 58 82 84 36 45 59 69 238 0 51 67 63 33 54 137 38 62 64 64 84 99 45 107
Character a l p -p a p p r o a c h c -c s o y o u w i
Milliseconds 62 92 105 78 291 83 96 145 72 116 82 61 69 125 19 228 142 116 99 72 60 81 22 45 85
Character l l s e e h o w t h e y l e a d n a t u
Milliseconds 141 109 0 101 20 148 32 48 46 46 74 50 23 115 19 62 71 50 42 37 71 32 84 137 89
Character r a l l y t o t h e m a i n i d e a o f
Milliseconds 13 37 79 74 146 0 114 0 75 0 66 51 42 70 101 95 0 100 25 90 82 41 38 58 86
Character t h i s s -s c h a p t e r , t h e l i m i
Milliseconds 65 63 31 44 31 125 45 224 193 100 41 95 82 108 38 48 52 54 36 96 52 50 49 118 63
Character t . T h e i d e a o f a l i m i t p l
Milliseconds 103 124 38 71 80 80 80 38 49 105 30 36 51 79 75 72 70 83 45 69 94 79 86 24 105
Character a y s a f o u n d a t i o n a l r o l e t
Milliseconds 32 110 79 77 70 79 131 85 38 94 88 97 40 39 34 38 93 77 85 115 48 53 110 48 104
Character h r o u g h o u t c a l c u l u s .
Milliseconds 47 55 45 47 37 81 73 51 60 76 123 90 68 124 86 105 89 114 33
WPM Timing
Seconds WPM
1.74 82.63
3.49 123.95
5.23 119.36
6.97 129.11
8.71 126.7
10.46 117.06
12.2 120.01
13.94 119.64
15.68 117.83
17.43 117.75
19.17 114.56
20.91 111.9
22.65 109.65
24.4 110.18
26.14 105.59
27.88 106.3
29.63 110.18
31.37 109.41
33.11 107.64
34.85 107.42
36.6 106.9
38.34 109.86
40.08 109.88
41.82 113.05
43.57 114.03
45.31 113.88
47.05 114.77
48.79 113.13
50.54 109.46
52.28 109.95
54.02 108.18
55.77 108.88
57.51 110.38
59.25 112
60.99 111.75
62.74 112.66
64.48 111.48
66.22 110.9
67.96 110.18
69.71 110.35
71.45 110.85
73.19 112.14
74.93 112.74
76.68 112.37
78.42 114
80.16 115.86
81.91 116.33
83.65 117.49
85.39 118.33
87.13 118.99