Peter (peter12253)

Race #542

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Official speed 94.49 wpm (109.73 seconds elapsed during race)
Without ending ping 94.72 wpm (139 ms delay sending score to TypeRacer’s server)
Timerless 94.72 wpm (2 ms elapsed before first character typed; 109.59 seconds elapsed during race)
Timerless minus one 94.61 wpm, ignoring the first character typed
Race Start October 8, 2024 3:00:08pm UTC
Race Finish October 8, 2024 3:01:58pm UTC
Outcome No win (1 of 1)
Accuracy 96.5%
Points 255.12
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 Caclculus is a tool that helps us understand how a change in a one quanittity is related to a change in another. How does the speed of a falling object change as a fnctunction of time? How does ht the level of water in a barrled el 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 unmiveriverse, and powerful modern instruments help us see more and more. In this sedction we introduce the ideas of average nad and instantaneous rates of hcchance, ge, and show that they are clseoeslysely related to the slope of a coveurve at ta point P on the curve. We give precise developemments of these important concepts in the neext chapter, but ofr noor now we cuse an informal paapproach so you will see ho thewhoow they lead natrualralurally to the main idea of this capthapter, the limit. The idea of a limit plyasalays a foundational role throughout calculus.
Timing
Character C a c -c l c u l u s i s a t o o l t h a t
Milliseconds 2 276 92 474 183 86 104 131 81 94 91 68 185 97 87 91 87 35 135 152 63 71 40 67 56
Character h e l p s u s u n d e r s t a n d h o w
Milliseconds 32 83 115 50 109 97 71 59 116 94 99 150 34 176 79 101 150 80 130 199 171 140 41 87 82
Character a c h a n g e i n a - -a o n e q u a n i
Milliseconds 86 79 128 71 89 73 73 132 56 25 45 114 15 98 288 114 175 33 55 76 118 55 122 60 230
Character t -t -i t i t y i s r e l a t e d t o a c
Milliseconds 76 296 135 122 57 95 61 119 57 77 71 135 69 84 217 98 76 189 44 88 51 120 282 121 123
Character h a n g e i n a n o t h e r . H o w d o e
Milliseconds 47 101 43 581 108 69 46 34 85 109 73 48 116 101 69 15 100 110 291 104 80 77 101 101 48
Character s t h e s p e e d o f a f a l l i n g
Milliseconds 52 56 78 33 72 66 103 99 112 164 193 99 66 80 57 72 86 45 138 277 141 35 50 59 47
Character o b j e c t c h a n g e a s a f n c t -t -c
Milliseconds 139 183 76 104 169 72 33 148 82 66 92 58 119 119 138 83 141 110 96 537 382 83 84 216 123
Character -n u n c t i o n o f t i m e ? H o w d o e
Milliseconds 198 207 149 76 72 14 147 25 44 116 35 59 397 53 62 52 148 123 212 97 71 73 111 57 90
Character s h t - - -t -h t h e l e v e l o f w a
Milliseconds 42 72 76 4 178 86 218 102 99 141 122 86 76 47 48 74 124 35 47 135 91 50 76 53 85
Character t e r i n a b a r r l e d - -d -e -l e l c
Milliseconds 102 125 54 28 73 62 51 71 79 133 106 77 131 106 43 163 30 252 207 130 135 175 81 100 109
Character h a n g e a s a f u n c t i o n o f t h
Milliseconds 129 89 69 59 102 605 120 64 101 123 57 88 135 150 98 67 30 144 26 35 143 25 59 133 67
Character e a m o u n t o f l i q u i d p o u r e d
Milliseconds 95 68 147 158 284 56 179 48 64 29 109 44 269 208 195 80 69 176 118 329 198 105 143 105 204
Character i n t o i t ? W e s e e c h a n g e o
Milliseconds 90 89 35 104 59 108 132 68 167 132 170 150 89 107 56 139 77 134 81 54 96 61 83 56 177
Character c c u r r i n g i n n e a r l y e v e r y t
Milliseconds 112 131 110 112 318 153 52 60 79 85 40 66 149 100 30 69 48 64 122 85 208 74 69 52 103
Character h i n g w e o b s e r v e i n t h e w o
Milliseconds 118 117 55 28 82 82 35 93 232 131 286 52 52 176 43 99 75 42 54 87 30 96 91 182 49
Character r l d a n d u n m i v e r -r -e -v -i -m i v e r s
Milliseconds 84 81 91 71 91 31 75 59 57 182 15 4 25 117 92 208 176 131 142 138 173 109 89 86 84
Character e , a n d p o w e r f u l m o d e r n i n
Milliseconds 80 49 111 80 44 66 79 39 146 52 11 34 160 19 85 75 126 21 121 173 27 90 117 85 64
Character s t r u m e n t s h e l p u s s e e m o r
Milliseconds 132 60 138 42 146 53 90 63 83 90 103 87 66 90 80 201 91 76 131 90 168 93 119 72 55
Character e a n d m o r e . I n t h i s s e d -d c
Milliseconds 32 62 53 77 77 48 99 5 87 67 29 103 108 154 83 59 31 89 73 62 131 192 10 518 136
Character t i o n w e i n t r o d u c e t h e i d e
Milliseconds 62 64 153 23 53 151 35 114 185 35 94 129 63 290 105 99 142 31 122 0 90 62 59 113 124
Character a s o f a v e r a g e n a d -n -a -d - a n d
Milliseconds 79 128 153 11 162 121 327 165 129 61 89 86 96 41 100 65 56 44 579 0 0 0 255 119 93
Character i n s t a n t a n e o u s r a t e s o f h
Milliseconds 81 65 45 290 159 360 114 101 308 107 194 170 57 100 81 151 74 95 63 89 16 70 71 59 135
Character c -c -h c h a n c e , - -, -e -c g e , a n d s h
Milliseconds 64 346 128 92 93 79 77 93 179 87 82 194 176 136 130 172 151 104 67 122 33 87 52 102 72
Character o w t h a t t h e y a r e c l s e -e -s o e
Milliseconds 42 98 85 160 102 45 61 53 92 65 121 31 80 80 42 48 41 174 103 142 23 408 145 187 129
Character s l y -y -l -s -e s e l y r e l a t e d t o t h
Milliseconds 0 58 105 303 111 113 138 136 52 194 131 127 75 57 106 99 48 87 174 53 75 46 86 56 43
Character e s l o p e o f a c o v e -e -v -o u r v e
Milliseconds 84 73 114 88 138 68 69 67 38 83 54 110 66 515 58 133 62 331 97 120 284 182 227 74 111
Character a t t -t a p o i n t P o n t h e c u r
Milliseconds 92 83 81 65 449 84 97 135 148 88 16 19 72 138 125 156 59 66 65 20 61 90 131 127 25
Character v e . W e g i v e p r e c i s e d e v e l
Milliseconds 235 24 97 105 420 164 91 135 125 87 47 67 128 87 39 271 197 118 27 89 185 146 143 82 38
Character o p e m -m -e m e n t s o f t h e s e i m p o
Milliseconds 150 52 220 33 372 121 392 68 75 54 80 75 46 94 37 475 99 93 93 78 87 141 69 41 148
Character r t a n t c o n c e p t s i n t h e n e e
Milliseconds 90 144 88 46 74 100 110 36 21 130 217 90 56 109 86 125 34 37 80 37 58 130 156 64 98
Character -e x t c h a p t e r , b u t o f r n o -o -r
Milliseconds 458 91 83 69 240 121 91 93 107 68 73 48 97 134 80 71 87 93 13 141 68 64 43 956 0
Character - -n -o o r n o w w e c -c u s e a n i n f
Milliseconds 0 0 0 74 62 73 48 52 64 170 114 87 93 144 263 295 83 36 60 77 66 102 107 60 309
Character o r m a l p a -a -p a p p r o a c h s o y o u
Milliseconds 106 71 138 129 66 91 200 11 314 122 133 93 138 132 107 185 169 67 86 150 32 88 104 67 57
Character w i l l s e e h o t h e $w -o - -t -h -e h o -o
Milliseconds 64 53 68 135 149 14 90 46 161 95 162 33 148 115 86 117 478 0 0 0 0 0 25 80 445
Character -w o w t h e y l e a d n a t r -r u a l -l -a -u
Milliseconds 326 49 101 119 110 78 114 55 123 30 52 59 116 67 249 83 95 165 457 151 99 238 263 80 123
Character r a l -l -a -r u r a l l y t o t h e m a i n
Milliseconds 96 57 126 292 124 125 230 110 66 78 139 81 76 55 56 86 63 43 70 85 66 129 54 31 62
Character i d e a o f t h i s c a p t -t -p -a h a p t e
Milliseconds 108 3 187 78 48 116 54 66 238 69 96 55 58 158 107 12 215 256 120 108 199 36 94 91 105
Character r , t h e l i m i t . T h e i d e a o f
Milliseconds 64 57 89 60 14 70 42 190 58 156 23 133 111 114 98 122 52 69 42 104 140 52 39 55 97
Character a l i m i t p l y a s -s -a -y -l a -a l a y s
Milliseconds 70 99 74 74 58 131 89 103 36 206 167 132 23 43 322 128 76 126 131 446 181 96 81 115 128
Character a f o u n d a t i o n a l r o l e t h r o u
Milliseconds 205 16 434 119 47 198 152 148 67 38 114 65 78 99 62 71 62 147 55 55 89 62 114 61 34
Character g h o u t c a l c u l u s .
Milliseconds 112 40 128 52 32 146 305 107 489 125 157 112 165 142 23
WPM Timing
Seconds WPM
2.19 76.55
4.39 106.63
6.58 109.36
8.78 99.79
10.97 101.71
13.17 102.07
15.36 105.46
17.56 108
19.75 99.03
21.95 101.71
24.14 100.91
26.33 98.43
28.53 98.01
30.72 99.6
32.92 98.43
35.11 99.79
37.31 100.68
39.5 101.77
41.7 101.59
43.89 102.8
46.08 103.9
48.28 106.13
50.47 105.56
52.67 105.26
54.86 104.11
57.06 102.84
59.25 101.46
61.45 101.75
63.64 100.12
65.84 100.43
68.03 99.31
70.22 98.43
72.42 98.76
74.61 99.07
76.81 97.96
79 98.73
81.2 98.72
83.39 97.56
85.59 97.73
87.78 96.92
89.98 97.49
92.17 96.08
94.36 94.99
96.56 94.33
98.75 94.78
100.95 94.98
103.14 95.4
105.34 94.21
107.53 94.86
109.73 94.49