Andrew (andrew_the_guy)

Race #248

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Official speed 94.53 wpm (109.68 seconds elapsed during race)
Without ending ping 94.62 wpm (102 ms delay sending score to TypeRacer’s server)
Timerless 94.92 wpm (343 ms elapsed before first character typed; 109.23 seconds elapsed during race)
Timerless minus one 94.81 wpm, ignoring the first character typed
Race Start September 14, 2023 2:20:32am UTC
Race Finish September 14, 2023 2:22:22am UTC
Outcome Win (1 of 5)
Opponents 2. cloudios (87.44 wpm)
3. lnstruments (87.30 wpm)
Accuracy 99.0%
Points 255.23
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 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 pourded into it? We see change occurring in nerarly everything we observe in the world an d universe, and powerful modern instruments help us see more and more. In this section we introduce the ideas of average and instantaneous crates of change, and show that they are closely related to the slope of a curve at a poing Pt P on the scurve. We give precise developments of thse ese important concepts in the next chapter, but for now we use an informal apporoach so you will see how they lead naturally to the main idea of this chapter, the limit. The idea of a limit plays a foundation al 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 343 251 355 139 157 69 141 124 81 127 62 73 108 85 163 61 160 199 86 109 93 19 91 97 146
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 81 109 124 97 95 69 89 95 141 182 51 187 50 123 112 95 32 120 84 77 79 16 107 79 98
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 114 80 137 99 100 118 82 48 77 64 152 84 30 47 183 64 137 130 130 111 93 157 125 142 31
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 76 136 75 110 206 114 64 190 88 134 93 80 102 111 189 73 146 119 108 125 80 122 63 95 141
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 124 86 130 109 81 34 115 103 298 179 77 122 171 126 64 78 62 153 95 63 76 95 108 95 141
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 186 81 147 64 430 91 129 185 99 96 179 121 61 86 68 160 226 153 106 155 196 77 162 119 97
Character n g e a s a f u n c t i o n o f t i m e
Milliseconds 110 87 180 63 132 134 109 89 103 120 121 198 84 187 61 40 88 141 131 112 82 164 105 92 80
Character ? H o w d o e s t h e l e v e l o f w
Milliseconds 221 221 245 264 97 71 154 96 108 60 78 156 105 86 76 162 113 204 171 108 93 152 66 144 190
Character a t e r i n a b a r r e l c h a n g e a
Milliseconds 59 190 199 65 122 150 46 497 133 95 243 175 109 153 91 132 82 219 101 112 92 114 150 105 231
Character s a f u n c t i o n o f t h e a m o u n
Milliseconds 81 83 95 93 194 87 184 77 208 72 56 63 478 191 77 66 181 77 105 50 312 94 257 106 215
Character t o f l i q u i d p o u r d -d e d i n t o
Milliseconds 45 89 153 63 78 143 77 217 109 67 119 89 252 28 97 93 257 338 79 165 83 207 63 66 117
Character i t ? W e s e e c h a n g e o c c u r r
Milliseconds 78 168 75 220 210 232 274 57 311 89 155 111 249 77 99 99 93 91 79 201 83 136 109 108 331
Character i n g i n n e r -r a r l y e v e r y t h i n
Milliseconds 94 68 71 94 236 87 111 292 94 106 548 132 166 108 171 134 116 183 156 47 206 148 123 83 120
Character g w e o b s e r v e i n t h e w o r l d
Milliseconds 64 83 149 121 65 201 89 201 50 107 208 161 68 188 76 74 270 110 79 58 164 107 105 119 76
Character a n - d u n i v e r s e , a n d p o w e
Milliseconds 65 98 96 62 453 111 67 188 192 79 64 163 71 139 78 119 124 93 113 60 90 182 64 108 49
Character r f u l m o d e r n i n s t r u m e n t s h
Milliseconds 86 201 105 93 99 182 51 98 176 61 77 106 140 77 48 93 170 82 217 93 109 48 81 92 121
Character e l p u s s e e m o r e a n d m o r e .
Milliseconds 94 96 131 133 122 72 79 128 104 156 131 168 62 51 79 67 172 89 82 77 119 64 47 56 135
Character I n t h i s s e c t i o n w e i n t r o
Milliseconds 90 276 300 108 53 93 74 134 47 180 114 187 199 71 46 64 82 154 64 56 152 61 77 193 95
Character d u c e t h e i d e a s o f a v e r a g e
Milliseconds 119 140 180 80 79 201 46 85 76 134 61 187 83 121 72 128 89 62 108 202 158 50 125 141 127
Character a n d i n s t a n t a n e o u s c -c r a t e
Milliseconds 55 120 84 78 63 95 92 31 128 138 110 187 128 225 133 200 75 66 70 311 313 100 203 131 79
Character s o f c h a n g e , a n d s h o w t h a
Milliseconds 65 56 120 62 79 126 113 107 111 85 334 128 118 118 117 58 70 132 89 72 105 27 180 85 61
Character t t h e y a r e c l o s e l y r e l a t e
Milliseconds 86 88 127 85 85 112 155 210 110 65 85 167 63 159 67 63 408 74 212 197 72 127 117 154 71
Character d t o t h e s l o p e o f a c u r v e
Milliseconds 192 82 118 90 105 111 63 77 33 174 83 179 23 125 60 142 34 75 93 117 284 93 113 213 120
Character a t a p o i n g P -P - -g t P o n t h
Milliseconds 83 108 101 84 81 109 128 69 77 45 73 73 175 308 159 150 303 104 388 209 144 50 60 109 119
Character e s -s c u r v e . W e g i v e p r e c i s
Milliseconds 21 98 125 281 92 136 51 216 171 135 106 300 238 66 158 73 124 159 74 93 80 57 186 144 58
Character e d e v e l o p m e n t s o f t h s e - -e
Milliseconds 98 108 186 168 180 136 71 185 45 264 98 100 72 76 198 164 77 82 153 77 122 114 116 282 136
Character -s e s e i m p o r t a n t c o n c e p t s i
Milliseconds 163 106 146 101 93 177 135 45 64 119 168 67 124 55 83 235 35 80 89 83 178 95 76 80 197
Character n t h e n e x t c h a p t e r , b u t f
Milliseconds 52 101 126 84 60 74 106 275 209 156 118 143 93 184 124 331 190 46 106 83 213 168 63 108 136
Character o r n o w w e u s e a n i n f o r m a l
Milliseconds 80 70 94 109 73 48 69 155 80 63 189 77 77 68 135 102 98 158 50 92 118 70 353 140 99
Character a p p o -o r o a c h s o y o u w i l l s
Milliseconds 73 222 114 166 114 390 111 129 103 153 118 47 156 105 63 171 135 92 80 113 52 84 181 121 203
Character e e h o w t h e y l e a d n a t u r a l l
Milliseconds 93 151 128 167 59 86 76 213 57 111 104 96 152 79 94 132 125 88 304 94 170 77 78 98 149
Character y t o t h e m a i n i d e a o f t h i
Milliseconds 69 136 203 94 156 290 84 95 41 214 96 81 80 91 130 86 163 99 144 162 98 62 165 56 63
Character s c h a p t e r , t h e l i m i t . T h e
Milliseconds 133 26 190 76 115 99 279 180 29 134 90 167 47 93 78 95 62 192 107 114 144 78 307 249 32
Character i d e a o f a l i m i t p l a y s a
Milliseconds 72 180 72 175 96 166 125 89 82 537 55 247 58 216 99 114 64 180 111 168 121 93 133 100 119
Character f o u n d a t i o n - a l r o l e t h r o u
Milliseconds 118 490 62 167 36 106 86 102 37 83 67 462 163 152 105 187 61 180 96 73 207 91 94 77 50
Character g h o u t c a l c u l u s .
Milliseconds 93 111 183 58 63 75 223 106 93 140 100 97 128 141 57
WPM Timing
Seconds WPM
2.19 76.59
4.39 93
6.58 105.76
8.77 108.04
10.97 108.32
13.16 106.67
15.36 104.72
17.55 103.26
19.74 103.94
21.94 101.75
24.13 100.96
26.32 98.92
28.52 99.31
30.71 97.3
32.9 97.01
35.1 95.39
37.29 95.57
39.48 93.3
41.68 93.29
43.87 93.27
46.07 93
48.26 93.74
50.45 94.66
52.65 95.73
54.84 95.84
57.03 96.36
59.23 97.05
61.42 95.93
63.61 96.39
65.81 97.01
68 96.7
70.19 97.1
72.39 95.98
74.58 95.41
76.78 95.34
78.97 95.28
81.16 94.33
83.36 95.01
85.55 94.4
87.74 95.05
89.94 94.47
92.13 94.69
94.32 94.65
96.52 94.74
98.71 95.06
100.91 95.02
103.1 94.74
105.29 94.48
107.49 94.23
109.68 94.53