From the river to the sea (drarthwrarder)

Race #3897

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Official speed 88.04 wpm (117.76 seconds elapsed during race)
Without ending ping 88.22 wpm (235 ms delay sending score to TypeRacer’s server)
Timerless 88.59 wpm (491 ms elapsed before first character typed; 117.04 seconds elapsed during race)
Timerless minus one 88.48 wpm, ignoring the first character typed
Race Start November 9, 2023 8:04:21am UTC
Race Finish November 9, 2023 8:06:19am UTC
Outcome No win (2 of 2)
Opponents 1. rajat_das777 (92.74 wpm)
Accuracy 96.3%
Points 237.70
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 Cacllculus is a tool that helps us understand how a change in one quantity is related to a change ina another. Ho w does the speed of a flalalling object change a s a functio nn of time.? DHow does the level fo waof water in a barrell change ofas a function of the amount of liqiruid poured in to it? We see a change occuerrring in enarlnearly everything we observe in the worlsd and universe, and powerful modern instruments help us see mmorore and more. In this sectio nwe n we introduce the ideas of average and instantaneous rates of change, and show that they are closely related to hte slthe slope of a scurve at a point P on the curve. We give prcecise developments of these important concepts in teh nehe next chapter, but for now we use an informal approach tso you will see how they lead naturally to the main idea of this chapter, the limit. The idea of a limit plays af foundational role thoruroughout calculsuse.
Timing
Character C a c l -l -c l c u l u s i s a t o o l t h
Milliseconds 491 412 172 83 427 143 181 116 106 635 159 115 107 73 76 76 71 111 119 79 153 151 108 101 92
Character a t h e l p s u s u n d e r s t a n d h o
Milliseconds 76 72 72 44 90 77 139 77 75 83 89 112 114 129 75 99 75 117 86 82 75 84 70 88 123
Character w a c h a n g e i n o n e q u a n t i t
Milliseconds 102 37 78 111 111 75 87 74 110 116 75 40 114 113 72 74 72 77 294 78 113 113 132 91 96
Character y i s r e l a t e d t o a c h a n g e
Milliseconds 197 208 199 114 33 93 113 35 73 121 124 104 111 101 75 122 65 110 130 111 78 73 110 86 113
Character i n a - -a a n o t h e r . H o - w d o e
Milliseconds 38 117 72 44 432 137 76 114 70 87 122 102 112 70 83 150 183 101 203 278 83 76 158 77 110
Character s t h e s p e e d o f a f l a l -l -a -l a
Milliseconds 85 76 87 80 36 75 94 74 106 121 215 114 202 114 66 507 111 115 85 101 263 212 131 153 70
Character l l i n g o b j e c t c h a n g e a - s
Milliseconds 138 165 137 103 74 41 119 625 194 109 110 172 77 163 111 50 79 107 105 115 78 102 410 113 37
Character a f u n c t i o n -n - n o f t i m e . -. ?
Milliseconds 110 110 123 154 129 122 202 35 145 74 40 370 586 193 80 117 117 31 142 128 88 83 185 343 228
Character D -D H o w d o e s t h e l e v e l f o
Milliseconds 154 146 259 146 113 117 70 112 76 112 56 115 84 23 90 71 77 116 137 145 72 113 108 35 113
Character w a -a -w - -o -f o f w a t e r i n a b a r r
Milliseconds 77 95 204 153 127 138 127 226 71 84 85 116 112 100 73 43 109 98 325 120 112 111 445 164 165
Character e l l -l c h a n g e o f -f -o a s a f u n c
Milliseconds 149 124 134 418 82 221 114 36 79 78 98 77 116 74 254 128 37 79 74 91 75 115 110 112 111
Character t i o n o f t h e a m o u n t o f l i q
Milliseconds 190 36 147 74 38 135 76 74 92 39 73 76 111 70 112 110 79 110 71 77 111 71 101 114 219
Character i r -r -i u i d p o u r e d i n - t o i t ?
Milliseconds 227 116 304 138 232 131 143 74 249 218 160 149 77 120 73 73 133 111 355 113 109 109 95 76 207
Character W e s e e a - -a c h a n g e o c c u e r
Milliseconds 148 182 192 151 114 168 132 85 125 107 160 143 112 106 40 109 76 106 77 75 149 135 93 94 154
Character -r -e r r i n g i n e n a r l -l -r -a -n -e n e a r
Milliseconds 176 139 74 126 108 118 37 82 70 79 73 103 37 110 112 74 224 149 130 129 148 174 34 114 108
Character l y e v e r y t h i n g w e o b s e r v e
Milliseconds 77 156 85 86 147 168 35 181 155 141 79 140 74 75 175 76 77 125 111 122 120 99 123 171 73
Character i n t h e w o r l s -s d a n d u n i v e r
Milliseconds 129 122 72 190 77 108 71 115 88 57 119 76 508 37 113 35 117 72 114 75 104 117 38 109 74
Character s e , a n d p o w e r f u l m o d e r n i
Milliseconds 88 112 76 139 129 112 80 77 228 211 113 40 73 153 115 160 82 205 115 110 115 74 75 104 75
Character n s t r u m e n t s h e l p u s s e e m m
Milliseconds 125 37 146 449 141 181 121 91 70 138 113 71 119 75 173 115 84 92 69 168 145 141 80 34 114
Character o r -r -o -m o r e a n d m o r e . I n t h i
Milliseconds 150 118 233 154 125 190 35 77 83 71 71 78 75 75 85 80 71 111 109 221 155 158 120 21 100
Character s s e c t i o n w e - -e -w -n - n w e i n
Milliseconds 77 40 127 114 125 210 74 164 67 0 101 74 72 275 149 142 277 165 218 77 109 74 74 135 112
Character t r o d u c e t h e i d e a s o f a v e r
Milliseconds 33 133 94 120 134 73 133 74 113 36 114 34 90 70 108 102 110 73 89 74 73 75 153 145 75
Character a g e a n d i n s t a n t a n e o u s r a t
Milliseconds 95 100 121 74 64 77 73 71 76 108 322 135 96 73 112 117 318 148 120 148 76 71 112 87 123
Character e s o f c h a n g e , a n d s h o w t h
Milliseconds 116 117 79 82 116 30 159 116 36 110 70 124 112 113 285 77 113 84 69 115 82 44 412 149 83
Character a t t h e y a r e c l o s e l y r e l a t
Milliseconds 75 70 80 89 39 114 38 121 82 73 73 77 91 76 110 108 396 107 113 74 117 71 77 115 78
Character e d t o h t e s l -l -s - -e -t -h t h e s l o
Milliseconds 145 119 77 261 116 111 95 40 77 70 106 35 265 156 131 137 140 138 110 92 81 69 90 67 120
Character p e o f a s -s c u r v e a t a p o i n
Milliseconds 142 72 78 103 73 87 110 71 130 348 110 149 89 186 162 66 168 221 110 70 119 109 153 110 99
Character t P o n t h e c u r v e . W e g i v e
Milliseconds 41 76 224 117 411 437 141 89 76 85 64 105 78 91 170 148 115 73 255 121 157 103 78 114 126
Character p r c -c e c i s e d e v e l o p m e n t s o
Milliseconds 73 116 33 205 331 78 99 116 79 115 109 269 153 125 152 117 129 182 163 115 90 113 176 324 119
Character f t h e s e i m p o r t a n t c o n c e p t
Milliseconds 112 73 100 67 75 144 70 39 75 122 109 133 0 129 102 116 77 75 109 77 72 146 170 113 76
Character s i n t e h n e -e -n - -h -e h e n e x t c
Milliseconds 134 72 120 113 75 78 106 31 92 65 71 256 145 137 149 350 195 90 237 193 71 148 140 73 143
Character h a p t e r , b u t f o r n o w w e u s
Milliseconds 113 74 113 113 100 65 76 113 148 97 121 65 95 75 76 74 76 76 118 23 125 71 78 89 109
Character e a n i n f o r m a l a p p r o a c h t -t
Milliseconds 73 134 75 154 124 108 90 73 73 127 122 91 274 115 214 114 152 114 73 74 99 108 80 147 260
Character s o y o u w i l l s e e h o w t h e y
Milliseconds 78 131 115 164 70 74 76 81 116 128 127 76 113 114 122 118 87 91 78 41 121 34 105 66 89
Character l e a d n a t u r a l l y t o t h e m a i
Milliseconds 109 68 111 105 79 89 120 112 83 71 144 112 150 115 79 100 106 66 112 81 78 74 34 109 76
Character n i d e a o f t h i s c h a p t e r , t
Milliseconds 96 75 92 78 121 78 115 106 113 76 167 112 75 72 77 92 148 120 116 112 112 112 40 75 109
Character h e l i m i t . T h e i d e a o f a l
Milliseconds 77 78 108 208 214 135 96 95 109 108 184 77 75 74 51 68 131 77 107 121 109 69 37 109 113
Character i m i t p l a y s a f - -f f o u n d a t i
Milliseconds 119 111 107 74 75 242 167 82 113 174 138 563 183 84 400 131 118 173 78 69 116 73 89 120 75
Character o n a l r o l e t h o r u -u -r -o r o u g h o u
Milliseconds 87 71 36 220 0 453 114 128 76 40 109 75 90 108 39 321 154 122 112 87 77 112 77 178 110
Character t c a l c u l s -s u s e -e .
Milliseconds 113 37 142 109 83 109 113 138 120 242 170 76 71 488 200
WPM Timing
Seconds WPM
2.36 25.47
4.71 63.69
7.07 86.61
9.42 91.71
11.78 98.84
14.13 93.41
16.49 94.62
18.84 89.16
21.2 87.75
23.55 84.58
25.91 81.98
28.26 83.22
30.62 81.52
32.97 79.7
35.33 80.84
37.68 82.16
40.04 81.22
42.4 80.67
44.75 80.71
47.11 79.74
49.46 80.55
51.82 81.29
54.17 82.4
56.53 83
58.88 82.74
61.24 83.87
63.59 82.27
65.95 84.07
68.3 84.68
70.66 85.59
73.01 86.45
75.37 86.77
77.72 85.84
80.08 85.71
82.44 85.59
84.79 85.62
87.15 85.65
89.5 86.35
91.86 85.7
94.21 85.72
96.57 86.74
98.92 86.61
101.28 87.56
103.63 88.47
105.99 89.1
108.34 89.6
110.7 89.43
113.05 89.05
115.41 88.69
117.76 88.04