Jack (touvski)

Race #5673

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Official speed 77.60 wpm (133.61 seconds elapsed during race)
Without ending ping 77.77 wpm (299 ms delay sending score to TypeRacer’s server)
Timerless 78.08 wpm (520 ms elapsed before first character typed; 132.79 seconds elapsed during race)
Timerless minus one 77.99 wpm, ignoring the first character typed
Race Start December 28, 2024 4:21:42pm UTC
Race Finish December 28, 2024 4:23:56pm UTC
Outcome No win (3 of 5)
Opponents 1. buri_was_taken (115.27 wpm)
4. paradoxfox (76.10 wpm)
Accuracy 97.5%
Points 209.51
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 qunatantity is related ato a change in another. How does the speed of a falling object change as a function of time? How does the leve of l of water in a barrel change as a fun ctiction of the amoung ot of liquid poured into it? We see change coccurinring in nearly everything we observe in the world and univeserse, and poewrwerful modern intrustruments help us see more and more. In this section we introduce the ideas of average and oininstantaneous rates of change, and show that they are closely related to he the slpoope ofaf a curve atg a a point P on the curve. We give precies ise 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, shthe liit.llimit. The idea ofa a limit plays a foundational 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 520 115 92 226 90 133 114 140 106 115 74 68 154 39 273 82 161 157 90 114 67 29 104 19 176
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 102 65 91 160 82 178 96 81 203 171 84 203 91 151 106 147 12 117 184 245 100 125 101 128 80
Character c h a n g e i n o n e q u n a t -t -a -n a n t
Milliseconds 191 79 100 69 77 131 67 80 59 106 140 72 177 43 353 49 216 67 143 383 146 155 88 103 130
Character i t y i s r e l a t e d a -a t o a c h a
Milliseconds 64 143 145 104 136 131 55 457 74 167 74 102 98 165 103 146 320 123 94 101 128 77 138 96 74
Character n g e i n a n o t h e r . H o w d o e s
Milliseconds 109 69 110 72 144 38 117 146 82 51 133 94 49 57 146 109 332 146 74 92 261 42 125 97 69
Character t h e s p e e d o f a f a l l i n g o b
Milliseconds 553 55 51 92 83 84 76 163 163 64 116 59 191 1346 105 138 36 82 167 78 61 143 42 198 163
Character j e c t c h a n g e a s a f u n c t i o n
Milliseconds 193 94 204 114 99 227 91 104 79 48 95 66 113 79 138 64 102 132 135 168 78 152 21 52 55
Character o f t i m e ? H o w d o e s t h e l e
Milliseconds 97 129 88 78 186 40 55 67 272 164 270 135 49 109 117 73 118 71 121 112 95 62 59 107 66
Character v e o f - -f -o - l o f w a t e r i n a
Milliseconds 171 142 88 227 77 89 485 143 155 137 248 91 132 79 64 152 77 131 90 107 104 112 22 143 97
Character b a r r e l c h a n g e a s a f u n c
Milliseconds 73 180 123 94 172 101 74 202 275 98 61 108 33 87 95 119 147 114 126 79 134 103 171 30 68
Character t i -i -t -c - c t i o n o f t h e a m o u n g
Milliseconds 152 18 529 132 187 159 327 194 79 60 28 123 268 111 65 295 56 109 53 160 130 146 108 209 77
Character o -o - -g t o f l i q u i d p o u r e d i
Milliseconds 69 156 410 155 150 95 58 425 112 71 167 57 337 56 51 126 113 185 163 251 172 75 187 107 121
Character n t o i t ? W e s e e c h a n g e c -c o
Milliseconds 44 106 71 108 104 74 245 204 192 106 130 121 52 181 69 149 93 34 141 37 105 67 217 369 218
Character c c u r i n -n -i r i n g i n n e a r l y e v
Milliseconds 86 149 72 133 106 69 460 138 106 111 33 89 95 106 32 121 174 51 90 81 135 106 126 204 145
Character e r y t h i n g w e o b s e r v e i n t h
Milliseconds 125 70 93 147 77 55 133 59 76 139 67 105 179 176 228 55 466 184 127 103 66 68 87 155 91
Character e w o r l d a n d u n i v e s e -e -s r s e ,
Milliseconds 70 44 168 50 92 113 54 98 136 101 72 105 122 174 93 101 162 209 72 462 133 106 95 83 122
Character a n d p o e w r -r -w -e w e r f u l m o d e r
Milliseconds 136 147 83 103 60 226 90 96 4 106 417 143 147 52 46 68 365 11 103 135 184 96 173 193 77
Character n i n t r u -u -r -t s t r u m e n t s h e l p
Milliseconds 143 97 111 83 154 185 100 389 140 142 113 93 186 76 197 92 106 100 121 130 182 105 82 114 87
Character u s s e e m o r e a n d m o r e . I n
Milliseconds 483 73 86 255 62 202 97 70 69 54 72 44 89 199 102 108 132 67 81 56 103 97 216 144 48
Character t h i s s e c t i o n w e i n t r o d u c e
Milliseconds 164 46 45 84 64 222 60 222 164 55 44 71 64 193 50 146 334 144 82 202 126 243 83 164 225
Character t h e i d e a s o f a v e r a g e a n d
Milliseconds 72 142 48 79 60 152 121 205 51 322 211 126 101 60 651 161 149 145 85 205 99 90 123 115 55
Character o i n -n -i -o i n s t a n t a n e o u s r a t e
Milliseconds 98 131 32 20 483 154 154 195 52 54 100 40 339 751 177 193 86 143 89 149 130 461 77 156 67
Character s o f c h a n g e , a n d s h o w t h a
Milliseconds 154 155 145 84 44 184 106 77 88 67 112 110 113 173 144 65 106 137 39 68 96 125 573 78 41
Character t t h e y a r e c l o s e l y r e l a t e
Milliseconds 68 51 220 105 55 123 99 172 118 65 71 151 33 167 44 90 211 133 47 192 93 189 107 252 83
Character d t o h e - -e -h t h e s l p o -o -p o p e
Milliseconds 160 113 126 67 82 289 129 120 286 155 138 89 135 61 59 283 58 155 208 352 127 218 89 92 91
Character o f a f -f -a a c u r v e a t g a - -a - -g
Milliseconds 94 72 188 59 403 178 142 85 91 245 82 143 207 123 93 117 73 88 50 101 77 412 139 160 158
Character a p o i n t P o n t h e c u r v e .
Milliseconds 87 101 72 219 119 63 110 105 255 195 129 241 52 113 142 89 69 59 380 65 712 232 102 115 105
Character W e g i v e p r e c i e s - -s -e -i i s e d
Milliseconds 268 49 178 149 107 125 135 34 194 105 33 206 79 140 90 141 328 150 150 180 866 96 49 90 732
Character e v e l o p m e n t s o f t h e s e i m p o
Milliseconds 176 133 101 122 183 84 844 130 193 134 138 225 171 77 59 180 38 66 106 97 80 201 39 616 114
Character r t a n t c o n c e p t s i n t h e n e x
Milliseconds 114 190 122 2 92 112 283 56 66 105 186 93 95 171 96 172 65 77 145 79 45 66 161 62 176
Character t c h a p t e r , b u t f o r n o w w e
Milliseconds 106 127 256 72 83 70 187 141 105 104 95 244 82 134 84 238 51 148 92 221 62 67 82 1416 50
Character u s e a n i n f o r m a l a p p r o a c h
Milliseconds 111 144 90 62 90 316 134 93 105 81 103 116 97 102 86 87 89 238 142 154 244 67 135 227 154
Character s o y o u w i l l s e e h o w t h e y
Milliseconds 123 139 100 89 189 89 54 146 141 64 44 161 81 141 68 182 113 49 78 61 83 233 56 138 51
Character l e a d n a t u r a l l y t o t h e m a
Milliseconds 111 154 64 72 179 89 304 79 110 99 103 60 100 156 154 408 169 56 100 94 84 58 64 163 37
Character i n i d e a o f t h i s c h a p t e r ,
Milliseconds 88 58 126 256 119 188 77 187 128 68 66 168 52 48 54 74 454 92 67 105 98 108 103 78 111
Character s h -h -s t h e l i i t . -. l -l -i -i -t -l l i m i t
Milliseconds 283 51 679 117 142 113 88 61 706 153 178 124 140 461 309 345 0 0 0 0 372 130 105 132 117
Character . T h e i d e a o f a - -a a l i m i t
Milliseconds 138 134 175 181 40 95 153 167 200 77 312 122 84 169 47 474 144 123 1139 101 286 63 204 56 95
Character p l a y s a f o u n d a t i o n a l r o l
Milliseconds 72 115 178 96 104 122 233 108 59 147 81 67 199 17 118 121 58 55 50 343 112 97 271 76 165
Character e t h r o u g h o u t c a l c u l u s .
Milliseconds 76 93 179 66 110 72 56 100 100 122 77 63 106 232 103 162 540 51 125 118 117 100
WPM Timing
Seconds WPM
2.67 80.83
5.34 94.31
8.02 95.8
10.69 85.32
13.36 86.22
16.03 87.57
18.71 83.4
21.38 85.89
24.05 88.32
26.72 87.12
29.39 86.96
32.07 86.82
34.74 84.63
37.41 82.44
40.08 82.93
42.75 82.52
45.43 82.68
48.1 82.83
50.77 84.14
53.44 82.41
56.12 81.9
58.79 81.45
61.46 82.59
64.13 83.08
66.8 82.99
69.48 81.87
72.15 81.17
74.82 82.12
77.49 82.54
80.16 81.88
82.84 80.98
85.51 79.99
88.18 80.02
90.85 79.64
93.53 78.01
96.2 77.22
98.87 77.31
101.54 78.12
104.21 78.42
106.89 77.91
109.56 78.31
112.23 79.12
114.9 79.48
117.58 79.91
120.25 78.94
122.92 77.81
125.59 77.39
128.26 77
130.94 77.44
133.61 77.6