Ethan (sweethan)

Race #3275

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Official speed 96.84 wpm (107.06 seconds elapsed during race)
Without ending ping 97.24 wpm (313 ms delay sending score to TypeRacer’s server)
Timerless 98.27 wpm (1,122 ms elapsed before first character typed; 105.63 seconds elapsed during race)
Timerless minus one 98.16 wpm, ignoring the first character typed
Race Start February 21, 2024 1:35:23am UTC
Race Finish February 21, 2024 1:37:10am UTC
Outcome No win (2 of 3)
Accuracy 97.7%
Points 261.47
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 Clalculus is a tool. that helps us understand how a chnange in one quanititity is related to a change in another. How does the speed of a falling object change as a function of time time? How does the level o f water in a barrel change as a function of the amount of liquid pourdeed into it? QWWe see change occruyurring in nearly ever7thything 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 rategs s iof cof change, and show that they are closelry related to the slope o af a cuyrurve at a point P on the curve. We give precise d3eveevelopm,entents of these important concenpts in the next chapter, mbutbut for now we use an informal approach so you will see how they lead naturally to the main idea of this chapter,m th the limit. The idea of a limit plays a foundational role throughou8t t calcluulus.
Timing
Character C l -l a l c u l u s i s a t o o l . - -.
Milliseconds 1122 99 415 108 85 141 113 176 170 120 103 107 91 62 99 56 127 54 130 195 0 126 299 126 137
Character t h a t h e l p s u s u n d e r s t a n d
Milliseconds 127 51 44 61 52 88 98 88 154 87 82 109 67 89 75 152 92 132 52 150 56 92 43 98 83
Character h o w a c h n -n a n g e i n o n e q u a
Milliseconds 101 38 45 81 96 114 123 79 177 346 84 105 101 28 76 93 72 51 165 44 47 82 409 109 91
Character n i t i -i -t -i t i t y i s r e l a t e d t o
Milliseconds 113 99 100 111 343 125 102 115 83 46 80 124 203 90 84 361 52 87 109 280 73 129 83 100 13
Character a c h a n g e i n a n o t h e r . H o w
Milliseconds 116 73 88 195 153 91 63 23 75 88 134 73 119 125 62 83 47 109 51 51 68 100 317 251 116
Character d o e s t h e s p e e d o f a f a l l
Milliseconds 107 122 59 93 52 83 104 31 74 78 54 90 74 102 125 79 159 67 51 106 32 176 100 37 130
Character i n g o b j e c t c h a n g e a s a f u
Milliseconds 176 45 47 83 135 93 227 69 76 158 124 125 59 72 58 51 43 91 100 53 83 73 85 128 81
Character n c t i o n o f t i m e $ -i -m -e - t i m e ?
Milliseconds 125 97 154 79 29 73 50 120 45 53 106 83 78 22 432 0 0 0 608 161 80 76 69 574 683
Character H o w d o e s t h e l e v e l o - f w
Milliseconds 226 227 87 136 240 62 67 78 55 83 83 49 54 114 67 83 74 89 195 201 116 353 37 79 100
Character a t e r i n a b a r r e l c h a n g e a
Milliseconds 129 55 151 29 103 88 48 72 50 89 102 93 55 135 73 63 120 127 82 68 39 27 72 116 47
Character s a f u n c t i o n o f t h e a m o u n
Milliseconds 86 76 103 79 128 79 128 95 155 77 78 25 77 119 67 80 75 88 72 89 66 86 133 48 129
Character t o f l i q u i d p o u r d e -e -d e d i n
Milliseconds 25 100 88 91 52 163 73 191 84 103 141 107 106 200 95 70 133 171 165 101 135 196 77 157 67
Character t o i t ? Q W -W -Q W e s e e c h a n g e
Milliseconds 27 93 97 110 70 211 136 229 0 379 148 209 249 128 91 157 173 151 144 58 119 38 50 48 138
Character o c c r u y -y -u -r u r r i n g i n n e a r l y
Milliseconds 158 90 362 199 82 27 373 126 148 189 70 107 108 24 72 80 91 48 50 112 92 50 37 85 78
Character e v e r 7 t h -h -t -7 y t h i n g w e o b s e
Milliseconds 72 132 152 123 76 82 104 106 296 103 151 160 125 100 109 71 71 106 147 170 81 229 141 171 76
Character r v e i n t h e w o r l d a n d u n i v
Milliseconds 98 159 96 109 83 50 93 55 136 48 126 54 139 46 87 66 88 92 65 72 57 152 175 102 96
Character e r s e , a n d p o w e r f u l m o d e r n
Milliseconds 175 77 125 77 160 94 96 87 52 84 58 153 65 0 90 152 56 81 120 132 77 96 152 52 83
Character i n s t r u m e n t s h e l p u s s e e
Milliseconds 74 62 76 24 76 138 78 153 73 55 48 87 78 77 100 88 154 257 151 94 81 123 154 103 101
Character m o r e a n d m o r e . I n t h i s s e
Milliseconds 128 82 42 74 60 56 110 24 109 80 83 44 51 143 153 174 221 71 155 52 58 41 89 75 127
Character c t i o n w e i n t r o d u c e t h e i d
Milliseconds 157 166 87 74 49 50 107 28 90 132 69 97 133 108 90 135 92 107 128 78 49 76 86 30 97
Character e a s o f a v e r a g e a n d i n s t a n
Milliseconds 129 72 81 55 116 234 104 332 128 147 76 127 80 72 81 78 84 52 79 112 72 93 185 68 61
Character t a n e o u s r a t e g s - -s -g s i o f c
Milliseconds 127 287 129 195 134 76 63 138 74 99 154 24 13 102 156 230 101 127 84 105 90 0 50 81 128
Character -c -i -o -f - o f c h a n g e , a n d s h o w
Milliseconds 359 120 0 0 0 312 92 107 169 82 68 63 50 64 102 99 96 108 76 109 96 62 57 42 163
Character t h a t t h e y a r e c l o s e l r -r y r
Milliseconds 169 100 74 53 58 82 80 71 86 103 94 34 54 108 177 130 127 41 54 89 242 441 93 124 99
Character e l a t e d t o t h e s l o p e o a -a -
Milliseconds 73 140 110 81 98 111 129 125 83 93 78 109 70 109 72 89 128 149 91 56 84 144 48 289 79
Character f a c u y r -r -y -u u r v e a t a p o i n
Milliseconds 114 126 45 132 104 128 30 75 329 102 149 514 72 200 50 104 126 80 101 43 87 59 225 49 72
Character t P o n t h e c u r v e . W e g i v e
Milliseconds 29 151 289 241 229 47 74 105 76 76 108 100 84 47 178 49 87 96 200 250 80 151 53 119 30
Character p r e c i s e d 3 e v e -e -v -e -3 e v e l o p m
Milliseconds 56 67 116 101 154 108 89 81 344 684 153 0 104 98 304 105 125 126 61 107 50 63 154 152 221
Character , e n t -t -n -e -, e n t s o f t h e s e i m p
Milliseconds 0 74 78 51 261 104 148 125 88 78 79 72 113 80 119 131 74 81 72 30 106 77 138 75 105
Character o r t a n t c o n c e n -n p t s i n t h e
Milliseconds 153 164 175 115 109 78 106 123 63 47 70 135 130 276 167 46 95 61 105 55 72 52 88 26 109
Character n e x t c h a p t e r , m b u t -m -b -u -t b u t
Milliseconds 99 76 202 102 104 122 53 74 91 358 123 53 60 81 0 156 53 48 312 0 0 0 339 223 98
Character f o r n o w w e u s e a n i n f o r m
Milliseconds 126 98 65 67 53 83 60 66 112 121 55 105 106 72 50 116 93 107 101 134 48 125 65 68 110
Character a l a p p r o a c h s o y o u w i l l s
Milliseconds 117 347 145 66 91 108 188 109 86 130 343 96 362 36 97 103 58 54 73 80 63 153 126 93 50
Character e e h o w t h e y l e a d n a t u r a l l
Milliseconds 80 177 101 154 79 40 85 54 86 70 108 51 90 43 98 59 53 83 124 127 110 94 148 19 149
Character y t o t h e m a i n i d e a o f t h i
Milliseconds 285 242 149 57 96 25 115 47 84 83 67 66 75 46 91 71 149 53 33 85 99 50 133 28 58
Character s c h a p t e r , m t h -t -h - -m t h e l i
Milliseconds 118 60 104 58 96 66 310 124 52 61 25 26 136 76 259 0 269 126 141 96 107 26 75 116 97
Character m i t . T h e i d e a o f a l i m i t
Milliseconds 74 134 94 113 138 392 178 71 84 57 96 152 49 59 109 95 53 80 62 202 96 101 109 140 128
Character p l a y s a f o u n d a t i o n a l r o l e
Milliseconds 37 150 64 106 99 87 46 132 151 81 53 128 72 127 56 103 61 70 118 168 191 192 96 113 71
Character t h r o u g h o u 8 t - -t -8 t c a l c l u -u
Milliseconds 81 78 81 51 63 76 49 88 83 102 0 78 129 325 102 125 64 79 95 104 133 97 106 80 274
Character -l u l u s .
Milliseconds 78 142 127 147 92 139
WPM Timing
Seconds WPM
2.14 28.02
4.28 53.24
6.42 80.33
8.57 88.27
10.71 81.82
12.85 84.06
14.99 88.07
17.13 94.57
19.27 98.38
21.41 96.39
23.55 90.69
25.7 92.47
27.84 93.98
29.98 97.67
32.12 99.01
34.26 97.72
36.4 94.94
38.54 92.78
40.68 93.5
42.83 93.03
44.97 94.74
47.11 96.04
49.25 97.22
51.39 98.54
53.53 99.53
55.67 99.8
57.81 100.25
59.96 99.07
62.1 98.36
64.24 99.57
66.38 98.89
68.52 98.77
70.66 97.31
72.8 97.58
74.94 97.83
77.09 95.89
79.23 94.97
81.37 95.71
83.51 95.99
85.65 94.99
87.79 95.95
89.93 95.54
92.07 96.57
94.22 96.8
96.36 97.76
98.5 97.22
100.64 97.3
102.78 97.84
104.92 97.67
107.06 96.84