Jack (jackschpeck)

Race #3534

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Official speed 83.80 wpm (123.72 seconds elapsed during race)
Without ending ping 83.90 wpm (147 ms delay sending score to TypeRacer’s server)
Timerless 84.16 wpm (386 ms elapsed before first character typed; 123.19 seconds elapsed during race)
Timerless minus one 84.07 wpm, ignoring the first character typed
Race Start December 1, 2023 4:45:22am UTC
Race Finish December 1, 2023 4:47:26am UTC
Outcome No win (2 of 5)
Accuracy 97.4%
Points 226.25
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 functionh of time? How does the level of water in a barrel change as a function of the amount ofl i liqueid poueredi into it? We see change cooooccuringrinring in rnnearly everything ewwe observe in the world and universe a, and powerful modern instruments help us see more and more. In this secitontion we introduce hthe ideas of average aned instantaneous rates of change, and show that they are closery lly related otto the slope of a curve at a point P on the curve. We kgive precise developments of these important concepts in the next chapter, but for now we use an informal appororoach so you will see how they lead tnanaturally oto the main idea of this chapter, the limit. The idea of a limit plays a foundation al role throughtouout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 386 237 264 218 78 276 98 178 121 38 301 175 458 100 102 78 124 200 102 61 97 73 45 108 62
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 143 63 157 103 95 62 129 156 76 176 60 142 121 99 77 83 104 120 60 102 80 120 80 102 100
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 123 77 176 52 76 57 56 100 84 126 82 53 83 94 470 22 270 99 161 57 136 61 109 119 82
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 76 125 80 127 67 130 53 223 102 96 127 123 477 161 80 78 102 83 54 85 53 63 81 108 93
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 86 82 100 52 109 82 100 119 120 115 121 187 151 82 104 168 102 98 57 505 81 76 143 58 115
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 171 102 100 80 108 34 120 217 129 53 141 123 99 17 89 141 83 80 103 175 80 101 212 91 85
Character n g e a s a f u n c t i o n h - -h o f
Milliseconds 99 82 78 56 86 192 85 94 105 53 65 180 62 106 80 83 56 21 124 396 98 141 81 99 100
Character t i m e ? H o w d o e s t h e l e v e l
Milliseconds 101 78 101 119 377 191 202 152 102 100 120 59 103 144 56 102 78 62 83 62 63 164 54 144 794
Character o f w a t e r i n a b a r r e l c h a n
Milliseconds 100 80 142 572 56 141 60 143 87 76 105 71 83 145 57 104 159 145 60 117 354 39 145 85 115
Character g e a s a f u n c t i o n o f t h e a
Milliseconds 58 65 84 76 216 79 81 116 146 347 321 134 141 82 56 80 170 142 123 80 122 20 140 80 101
Character m o u n t o f l i -i - -l l i q u e -e i d p
Milliseconds 60 57 164 152 60 80 41 138 97 29 29 524 96 126 122 76 37 265 60 144 570 180 52 87 140
Character o u e -e r e d i -i i n t o i t ? W e s e e
Milliseconds 105 160 202 342 58 62 216 80 451 140 41 99 102 113 83 147 426 522 218 174 174 106 101 138 537
Character c h a n g e c o -o o o -o -o -c o c c u r i n g -g
Milliseconds 155 103 71 128 83 55 64 83 230 98 260 182 140 296 90 156 234 98 125 117 84 137 83 102 301
Character -n -i -r r i n -n -i r i n g i n r n -n -r n e a r l
Milliseconds 118 123 130 138 124 77 339 103 169 141 118 119 58 124 84 189 54 192 241 124 230 59 102 99 124
Character y e v e r y t h i n g e w -w -e w e o b s e r
Milliseconds 100 117 83 160 77 163 183 235 79 78 144 39 142 101 179 286 117 80 110 133 207 94 181 63 186
Character v e i n t h e w o r l d a n d u n i v e
Milliseconds 212 76 103 118 65 79 55 192 29 106 54 119 64 144 427 99 162 102 101 80 37 164 82 59 59
Character r s e a -a - , a n d p o w e r f u l m o d
Milliseconds 183 116 86 193 111 315 99 202 198 106 83 121 57 83 159 38 280 145 177 39 124 100 122 82 120
Character e r n i n s t r u m e n t s h e l p u s s
Milliseconds 171 154 51 128 59 92 116 128 67 79 163 82 139 81 166 85 217 84 57 181 400 90 64 142 86
Character e e m o r e a n d m o r e . I n t h i s
Milliseconds 112 138 121 79 100 41 80 56 66 114 105 63 79 42 101 52 126 103 141 117 415 80 98 62 61
Character s e c i t o n -n -o -t -i t i o n w e i n t r o
Milliseconds 123 79 80 264 128 29 52 133 335 295 250 236 20 75 102 537 146 140 162 14 191 90 164 42 62
Character d u c e h -h t h e i d e a s o f a v e r a
Milliseconds 177 85 116 156 78 188 461 78 101 23 97 105 120 134 80 201 122 55 125 104 167 170 62 161 99
Character g e a n e -e d i n s t a n t a n e o u s r a
Milliseconds 144 77 101 55 167 184 500 226 157 106 118 101 120 56 209 299 80 160 58 121 105 72 128 136 85
Character t e s o f c h a n g e , a n d s h o w t
Milliseconds 215 80 169 82 78 105 79 216 129 118 104 120 38 100 124 101 59 120 82 355 53 79 86 94 61
Character h a t t h e y a r e c l o s e r y l -l - -y
Milliseconds 61 102 57 82 151 118 77 126 167 139 122 52 104 304 79 163 53 64 265 82 132 15 343 101 133
Character -r l y r e l a t e d o t -t -o t o t h e s l
Milliseconds 286 9 103 410 79 99 128 95 164 39 224 81 163 141 392 99 125 77 82 59 80 78 78 102 83
Character o p e o f a c u r v e a t a p o i n t
Milliseconds 157 451 75 105 314 78 105 68 113 136 82 142 196 80 78 122 392 80 102 103 97 62 120 101 79
Character P o n t h e c u r v e . W e k -k g i v
Milliseconds 59 188 117 102 106 101 78 79 100 81 195 130 82 214 53 142 165 590 261 226 159 311 79 121 101
Character e p r e c i s e d e v e l o p m e n t s o f
Milliseconds 22 93 147 84 54 282 51 167 82 80 220 145 149 76 124 693 208 196 100 134 63 272 112 102 145
Character t h e s e i m p o r t a n t c o n c e p t s
Milliseconds 45 118 19 140 165 82 81 121 101 80 94 89 158 79 102 55 140 118 41 128 141 188 130 484 201
Character i n t h e n e x t c h a p t e r , b u t
Milliseconds 181 75 79 118 42 102 78 120 64 83 746 179 82 282 42 117 123 51 87 152 72 129 101 49 152
Character f o r n o w w e u s e a n i n f o r m
Milliseconds 54 180 83 106 49 89 64 81 94 120 105 96 179 61 85 97 268 280 104 102 148 433 81 119 38
Character a l a p p o r o -o -r -o r o a c h s o y o u
Milliseconds 139 99 119 83 39 170 118 276 98 234 87 132 121 123 100 239 104 100 246 56 106 117 76 86 100
Character w i l l s e e h o w t h e y l e a d t n
Milliseconds 43 72 128 110 61 83 103 172 81 159 82 73 87 120 81 82 100 81 121 39 77 202 86 95 118
Character a -a -n -t n a t u r a l l y o -o t o t h e m a
Milliseconds 106 332 73 148 210 36 125 120 101 56 85 140 103 100 175 423 124 54 125 42 97 126 141 41 139
Character i n i d e a o f t h i s c h a p t e r ,
Milliseconds 78 77 145 81 141 153 79 141 143 59 98 83 36 58 84 85 80 93 43 204 101 55 145 97 63
Character t h e l i m i t . T h e i d e a o f a
Milliseconds 104 73 106 60 74 62 199 103 188 120 104 223 118 60 81 202 379 173 80 320 78 100 83 16 160
Character l i m i t p l a y s a f o u n d a t i o n
Milliseconds 81 81 198 80 180 82 119 169 101 139 408 123 80 254 141 78 82 185 36 102 180 59 56 103 188
Character - a l r o l e t h r o u g h t o u -u -o -t o u t
Milliseconds 469 180 13 144 82 82 171 43 93 105 56 142 60 102 103 142 101 158 125 279 103 134 222 58 82
Character c a l c u l u s .
Milliseconds 62 160 101 122 209 81 358 59 160 103
WPM Timing
Seconds WPM
2.47 58.19
4.95 80.02
7.42 95.37
9.9 96.99
12.37 97.96
14.85 96.99
17.32 99.76
19.8 101.23
22.27 97.53
24.74 96.51
27.22 96.11
29.69 95.78
32.17 94.75
34.64 91.79
37.12 89.23
39.59 88.5
42.07 84.44
44.54 82.17
47.01 81.93
49.49 81.23
51.96 82.44
54.44 81.56
56.91 82.86
59.39 84.06
61.86 83.61
64.34 82.44
66.81 82.62
69.28 81.92
71.76 82.44
74.23 83.41
76.71 83.38
79.18 82.44
81.66 82.15
84.13 82.58
86.61 82.58
89.08 82.44
91.56 82.05
94.03 82.82
96.5 82.32
98.98 83.17
101.45 83.27
103.93 82.67
106.4 83.68
108.88 82.99
111.35 83.63
113.83 84.23
116.3 84.3
118.77 84.46
121.25 84.22
123.72 83.8