Niels (nielsjensen)

Race #53425

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Official speed 115.10 wpm (90.08 seconds elapsed during race)
Without ending ping 115.54 wpm (237 ms delay sending score to TypeRacer’s server)
Timerless 115.77 wpm (184 ms elapsed before first character typed; 89.66 seconds elapsed during race)
Timerless minus one 115.64 wpm, ignoring the first character typed
Race Start November 14, 2023 5:57:10am UTC
Race Finish November 14, 2023 5:58:40am UTC
Outcome No win (2 of 5)
Opponents 1. forcherie2 (132.13 wpm)
3. wqkk (104.34 wpm)
4. talk_to_me_goose (101.04 wpm)
5. dx3906 (96.68 wpm)
Accuracy 97.6%
Points 310.78
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 o tto a change in another. how doHHow does the speed of a falling object change as a function of time? How does the leelvel of atwater in a barrel change as a function of the amount of liquid puoured into it? We see change occurring in nearly everything we oberserve in the world and unvierseiverse, and powerful modern instruenments help us see more and more. In this section we introduce the ideas of average and instantaneous rates of change, and show taht hthat they are closely related to the slope of acu curve at a point P on the curve. WE givee tive pgive precise development ofs of these oimprotantortant concepts in the next chapter, but for now we use an informal approach so you will see how they lead naturally to the main iea odea of this chapter, the limit. The idea of a limit plays a a f=dfoundational 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 184 568 104 377 72 109 80 97 72 316 137 34 116 68 60 51 111 158 79 21 63 31 85 22 66
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 86 76 56 70 47 87 102 13 83 121 63 133 34 56 105 26 44 141 42 59 43 79 54 73 81
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 89 63 48 66 71 63 46 53 47 58 62 65 103 13 220 74 135 32 114 69 113 15 84 48 112
Character r e l a t e d o t -t - -o t o a c h a n g
Milliseconds 50 120 42 43 88 55 39 159 38 65 120 34 252 102 109 100 83 49 81 90 50 85 62 45 57
Character e i n a n o t h e r . h o w d o -o -d - -w -o
Milliseconds 96 59 82 50 55 110 110 35 78 80 80 60 94 65 90 54 60 83 104 40 203 94 140 108 147
Character H -H -h H o w d o e s t h e s p e e d o f
Milliseconds 170 228 110 162 108 54 96 64 72 72 29 77 22 75 56 60 83 107 81 150 158 30 60 98 29
Character a f a l l i n g o b j e c t c h a n g e a
Milliseconds 118 43 124 89 38 348 247 31 55 45 38 113 61 103 143 106 57 169 29 55 86 81 28 61 77
Character s a f u n c t i o n o f t i m e ? H o w
Milliseconds 71 52 97 64 62 90 101 65 99 44 31 56 41 108 47 62 69 28 56 87 130 148 66 153 60
Character d o e s t h e l e e l -l -e v e l o f a t
Milliseconds 76 104 62 79 48 34 45 78 42 83 95 32 224 146 647 120 119 64 142 97 83 71 60 298 127
Character -t -a w a t e r i n a b a r r e l c h a n g
Milliseconds 234 112 39 56 51 95 53 90 74 64 48 74 108 35 124 99 169 71 101 58 110 75 9 83 33
Character e a s a f u n c t i o n o f t h e a m
Milliseconds 67 57 84 72 43 91 72 58 86 111 50 135 31 19 42 64 66 51 84 47 42 39 69 58 89
Character o u n t o f l i q u i d p u -u o u r e d i
Milliseconds 80 63 112 92 46 31 128 13 102 67 82 64 65 105 52 134 64 392 170 48 65 43 158 49 109
Character n t o i t ? W e s e e c h a n g e o c c
Milliseconds 41 56 52 67 75 65 174 114 70 126 118 70 75 132 93 153 29 53 110 33 36 65 79 61 133
Character u r r i n g i n n e a r l y e v e r y t h i
Milliseconds 111 81 121 79 40 81 37 84 26 68 122 23 50 21 122 89 71 123 102 109 52 81 104 15 87
Character n g w e o b e r -r -e s e r v e i n t h e
Milliseconds 57 80 57 60 84 30 91 116 197 24 301 130 52 59 47 160 97 94 59 59 75 133 58 66 86
Character w o r l d a n d u n v i e r s e -e -s -r -e -i -v i
Milliseconds 15 19 97 23 139 34 52 23 114 40 55 156 41 6 100 72 58 72 167 104 95 149 116 110 181
Character v e r s e , a n d p o w e r f u l m o d e r
Milliseconds 14 100 60 61 45 62 118 44 25 71 61 59 54 51 30 62 82 58 83 76 114 52 78 120 44
Character n i n s t r u e n -n -e m e n t s h e l p u s
Milliseconds 30 99 72 47 93 75 114 51 184 97 220 81 194 54 91 33 114 51 106 89 94 25 107 58 104
Character s e e m o r e a n d m o r e . I n t h
Milliseconds 95 101 68 145 55 46 47 58 30 58 31 38 83 48 51 52 56 51 56 95 89 149 64 55 44
Character i s s e c t i o n w e i n t r o d u c e t
Milliseconds 30 56 71 93 94 165 94 48 25 16 87 58 57 83 62 65 38 115 40 151 67 118 125 41 43
Character h e i d e a s o f a v e r a g e a n d i
Milliseconds 56 76 39 76 91 108 72 58 60 98 69 41 62 144 105 58 65 161 26 82 55 115 50 83 104
Character n s t a n t a n e o u s r a t e s o f c h a
Milliseconds 82 71 103 99 100 70 1102 194 108 127 52 92 73 103 109 74 66 67 30 112 118 19 109 57 47
Character n g e , a n d s h o w t a h t h -h - -t -h -a
Milliseconds 86 88 42 76 56 71 42 46 100 33 73 34 89 115 31 84 9 106 82 61 646 251 145 109 130
Character -t t h a t t h e y a r e c l o s e l y r e
Milliseconds 383 424 90 51 88 139 68 40 78 60 33 66 78 36 88 118 43 116 58 61 71 97 56 94 60
Character l a t e d t o t h e s l o p e o f a c u
Milliseconds 84 16 61 43 167 41 275 79 107 51 59 21 88 54 51 157 46 92 23 94 59 53 29 169 259
Character -u -c c u r v e a t a p o i n t P o n
Milliseconds 219 102 72 108 169 54 171 97 69 88 80 67 52 99 30 14 73 54 28 111 140 232 56 59 65
Character t h e c u r v e . W E g i v e -e -v -i -g - -E e
Milliseconds 51 41 44 51 99 79 80 147 119 97 89 102 42 90 75 92 75 51 170 102 113 131 120 126 54
Character t i v e p -p - -e -v -i -t g i v e p r e c i s e
Milliseconds 62 50 78 88 70 86 32 232 99 134 115 129 120 127 90 77 68 92 40 107 422 179 105 90 51
Character d e v e l o p m e n t o f -f -o - s o f t h
Milliseconds 96 260 155 102 72 63 159 68 71 69 103 52 76 61 91 373 102 123 84 82 116 86 68 63 46
Character e s e o -o i m p r o t a n t -t -n -a -t -o -r o r t a
Milliseconds 27 70 97 97 201 336 160 57 87 53 9 123 81 12 126 166 116 112 130 133 112 173 34 129 90
Character n t c o n c e p t s i n t h e n e x t c
Milliseconds 18 122 52 143 30 53 61 138 45 106 114 147 90 30 76 66 66 34 64 105 37 156 157 91 84
Character h a p t e r , b u t f o r n o w w e u s
Milliseconds 125 440 92 87 66 83 62 122 112 71 126 58 111 49 80 103 236 70 29 107 164 35 91 111 32
Character e a n i n f o r m a l a p p r o a c h s o
Milliseconds 84 42 121 88 84 39 61 63 112 62 136 70 87 59 100 59 150 91 116 17 101 83 115 154 117
Character y o u w i l l s e e h o w t h e y l e
Milliseconds 71 103 42 66 62 56 37 142 97 64 71 59 498 90 178 67 96 51 156 71 56 59 46 129 16
Character a d n a t u r a l l y t o t h e m a i n
Milliseconds 88 98 72 158 70 109 75 87 67 30 109 74 103 49 40 117 51 47 63 65 81 75 90 36 45
Character i e a o -o - -a $d e a o f t h i s c h a p t
Milliseconds 102 265 14 113 58 299 114 115 142 144 9 108 29 117 42 126 79 46 75 43 164 61 90 104 54
Character e r , t h e l i m i t . T h e i d e a o
Milliseconds 113 97 56 62 112 26 72 83 15 63 92 52 122 123 110 61 58 55 91 119 11 188 36 101 84
Character f a l i m i t p l a y s a a f -f - = d
Milliseconds 72 39 53 97 259 64 113 82 60 74 65 41 93 39 108 45 80 32 146 128 56 290 85 204 96
Character -d -= -a f o u n d a t i o n a l r o l e t h r o
Milliseconds 330 100 123 94 99 65 99 19 116 45 80 0 44 534 75 109 50 71 147 57 73 52 55 195 63
Character u g h o u t c a l c u l u s .
Milliseconds 61 125 112 77 109 148 212 171 44 67 183 49 77 120 95 138
WPM Timing
Seconds WPM
1.8 59.95
3.6 103.24
5.4 131
7.21 136.55
9.01 129.22
10.81 119.9
12.61 117.04
14.41 117.4
16.21 121.38
18.02 125.89
19.82 119.29
21.62 117.12
23.42 120.92
25.22 124.65
27.02 123
28.83 124.06
30.63 126.56
32.43 124.71
34.23 123.75
36.03 124.89
37.83 123.7
39.63 125.95
41.44 128
43.24 128.78
45.04 128.16
46.84 126.56
48.64 126.8
50.44 122.27
52.25 123.11
54.05 124.11
55.85 122.69
57.65 123.64
59.45 120.7
61.25 118.52
63.05 118.18
64.86 117.12
66.66 114.5
68.46 114.81
70.26 114.77
72.06 115.23
73.86 115.67
75.67 115.61
77.47 116.18
79.27 116.11
81.07 116.2
82.87 117
84.67 117.2
86.48 115.73
88.28 115.68
90.08 115.1