k (mc0sta)

Race #126470

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Official speed 89.49 wpm (115.86 seconds elapsed during race)
Without ending ping 89.74 wpm (326 ms delay sending score to TypeRacer’s server)
Timerless 90.55 wpm (1,037 ms elapsed before first character typed; 114.49 seconds elapsed during race)
Timerless minus one 90.45 wpm, ignoring the first character typed
Race Start November 11, 2023 7:33:22pm UTC
Race Finish November 11, 2023 7:35:18pm UTC
Outcome Win (1 of 5)
Opponents 2. dumpsterman (89.27 wpm)
3. tevefan (85.14 wpm)
4. pswongaa (79.09 wpm)
Accuracy 96.9%
Points 241.63
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 doees the level ofwat warter ein ain a barrel change saas a function of the amount of liquid poured into it? We see change occurring in nearly oeverything we observe in the world and univesrerse, and powerful modern instruments help us see more and more. In this section we introduce th eie ideas of average anda in instantaneous rates of change, and hwshow that hey theya re c are closely ralelated to the sholopo ee of a curve at a point P on the curve. We give precise delcelopvelopments of thse se ese imporanttant concetpspts in the next chapter, but fo rnr now we use an informal approach so you will see how they lead naturally to the main idea foof this chapter, the limit. The dieaidea of a limit plays a foundationa l role throgughout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 1037 152 137 263 112 162 140 135 57 54 106 90 87 108 126 86 128 202 140 197 58 45 41 56 139
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 90 134 108 209 94 165 82 55 142 193 55 207 82 495 25 136 46 100 127 141 74 34 106 73 104
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 93 59 67 80 121 44 137 94 64 51 253 73 94 68 134 109 96 105 144 65 97 67 99 101 103
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 107 270 22 142 99 122 94 143 120 167 31 94 37 125 118 67 53 79 423 119 62 74 59 81 237
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 89 68 100 81 50 62 85 47 293 102 50 158 144 56 111 79 57 171 32 49 35 166 71 121 141
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 149 40 63 109 78 0 178 127 79 448 150 56 73 83 64 120 146 79 90 161 110 143 275 24 55
Character n g e a s a f u n c t i o n o f t i m e
Milliseconds 121 49 86 129 61 95 197 56 151 336 90 162 397 400 56 41 59 104 85 123 60 141 47 67 22
Character ? H o w d o e e -e s t h e l e v e l o f
Milliseconds 228 34 338 103 113 31 233 100 70 405 369 64 104 509 35 65 41 126 69 167 72 112 45 118 63
Character w a t -t -a -w w a r -r t e r e i n a -a -e -i -n -
Milliseconds 123 102 177 196 145 138 53 66 73 139 470 61 40 88 17 11 183 71 56 97 237 150 0 0 0
Character i n a b a r r e l c h a n g e s a -a -s a s
Milliseconds 478 64 84 47 109 107 109 510 146 165 118 155 199 69 31 93 42 99 50 105 211 278 114 113 49
Character a f u n c t i o n o f t h e a m o u n t
Milliseconds 44 163 61 297 114 170 44 222 19 48 73 51 239 63 94 244 75 51 44 226 66 39 153 189 6
Character o f l i q u i d p o u r e d i n t o i t
Milliseconds 157 7 87 117 109 70 73 207 61 122 170 221 23 167 99 95 139 49 107 40 100 62 79 89 44
Character ? W e s e e c h a n g e o c c u r r i n g
Milliseconds 254 34 194 131 125 165 102 137 106 205 26 46 109 51 108 83 238 171 154 113 131 122 64 54 63
Character i n n e a r l y o -o e v e r y t h i n g w
Milliseconds 86 80 52 63 103 46 80 51 101 86 74 178 320 74 76 115 33 59 135 25 46 68 86 56 153
Character e o b s e r v e i n t h e w o r l d a n
Milliseconds 63 81 141 116 139 62 80 214 93 99 91 54 67 62 70 40 4 165 22 90 75 84 112 113 56
Character d u n i v e s r e -e -r -s r s e , a n d p o w
Milliseconds 65 28 506 155 55 66 96 130 10 32 396 145 131 66 73 90 108 50 136 55 89 68 283 92 51
Character e r f u l m o d e r n i n s t r u m e n t s
Milliseconds 21 112 153 54 101 41 214 18 161 192 72 75 76 104 83 75 57 118 20 247 119 73 108 74 141
Character h e l p u s s e e m o r e a n d m o r e
Milliseconds 227 81 77 72 97 94 99 66 216 290 130 32 95 42 80 16 69 80 60 70 36 89 52 58 54
Character . I n t h i s s e c t i o n w e i n t r
Milliseconds 78 20 227 76 66 125 57 35 49 51 220 31 254 133 71 40 34 92 132 42 163 245 52 91 126
Character o d u c e t h e i -e -i - e i d e a s o f
Milliseconds 67 416 51 97 140 57 150 16 82 5 114 344 0 138 310 168 168 36 149 51 135 61 95 122 91
Character a v e r a g e a n d a i n -n -i - -a i n s t a
Milliseconds 160 112 132 70 86 122 57 98 108 19 95 16 18 109 57 425 135 154 148 10 162 65 64 64 107
Character n t a n e o u s r a t e s o f c h a n g e ,
Milliseconds 120 335 82 318 98 151 65 101 58 242 100 95 60 100 26 111 92 32 151 18 83 96 204 148 96
Character a n d h -h w -w s h o w t h a t h e y - -y
Milliseconds 77 143 94 45 64 202 405 171 325 135 108 66 89 20 266 23 66 52 33 128 45 149 76 278 136
Character -e -h t h e y a r e c -c -r -e - - -a a r e c l
Milliseconds 142 141 112 54 41 108 78 0 96 29 79 161 234 165 0 0 164 168 99 66 73 31 79 148 42
Character o s e l y r a l -l -a e l a t e d t o t h e
Milliseconds 146 67 54 93 97 62 75 91 95 384 116 137 128 16 168 92 130 61 160 7 76 48 58 6 68
Character s h o -o -h l o p o e -e - -o e o f a c u r v
Milliseconds 71 106 31 388 114 165 165 114 140 6 0 448 148 143 83 0 141 74 93 40 108 114 63 139 193
Character e a t a p o i n t P o n t h e c u r
Milliseconds 90 79 75 118 58 56 121 40 81 83 80 46 100 318 314 122 88 57 61 106 8 72 329 99 92
Character v e . W e g i v e p r e c i s e d e l -l c
Milliseconds 449 92 132 41 464 865 123 228 71 93 64 117 92 151 118 270 88 114 21 144 203 119 147 433 67
Character e l o p -p -o -l -e -c v e l o p m e n t s o f t h
Milliseconds 131 89 190 87 269 151 163 126 146 23 113 84 207 81 173 156 105 56 82 63 46 102 62 119 52
Character s e - -e -s s e - -e -s e s e i m p o r a n t -t
Milliseconds 79 71 152 300 122 164 126 16 120 376 124 146 53 105 59 17 181 70 69 17 199 135 148 81 269
Character -n -a t a n t c o n c e t p s -s -p -t p t s i n
Milliseconds 160 159 59 65 53 89 73 158 74 53 79 188 90 175 121 222 142 132 171 20 129 67 103 43 77
Character t h e n e x t c h a p t e r , b u t f o
Milliseconds 26 89 18 27 202 55 189 161 70 214 87 16 186 55 121 41 43 72 286 40 135 30 151 9 165
Character r n -n -r - r n o w w e u s e a n i n f o
Milliseconds 4 235 355 135 136 28 59 129 45 82 208 153 37 146 345 95 101 71 265 89 76 126 51 300 75
Character r m a l a p p r o a c h s o y o u w i l l
Milliseconds 104 82 38 173 101 364 191 135 80 134 68 141 125 74 218 74 87 119 53 56 40 105 105 81 145
Character s e e h o w t h e y l e a d n a t u r a
Milliseconds 49 140 120 148 108 142 63 35 89 142 30 80 69 72 232 56 78 119 79 182 65 82 90 80 80
Character l l y t o t h e m a i n i d e a f o -o -f
Milliseconds 27 151 45 58 155 29 96 17 44 70 40 96 74 98 45 82 111 9 193 68 127 71 128 368 118
Character o f t h i s c h a p t e r , t h e l i m i
Milliseconds 146 72 42 201 38 34 105 116 295 142 131 124 103 137 44 234 43 99 72 23 76 134 62 76 69
Character t . T h e d i e a -d -i -e -a i d e a o f a
Milliseconds 133 86 58 164 74 51 46 219 0 204 67 303 0 0 0 282 37 180 76 77 87 73 105 30 185
Character l i m i t p l a y s a f o u n d a t i o n a
Milliseconds 236 60 107 76 136 36 96 101 69 154 82 48 145 38 302 47 77 153 40 63 164 35 45 44 94
Character - l r o l e t h r o g -g u g h o u t c a l
Milliseconds 119 446 172 90 103 54 137 53 94 185 111 156 122 222 572 202 101 145 175 93 97 31 303 56 116
Character c u l u s .
Milliseconds 299 67 212 40 355 87
WPM Timing
Seconds WPM
2.32 51.79
4.63 77.68
6.95 86.31
9.27 95.81
11.59 96.33
13.9 100.12
16.22 101.36
18.54 102.28
20.85 100.7
23.17 96.33
25.49 94.63
27.81 90.2
30.12 89.24
32.44 89.15
34.76 90.46
37.07 91.92
39.39 93.83
41.71 94.66
44.03 95.94
46.34 95.55
48.66 96.42
50.98 97.93
53.29 98.85
55.61 97.53
57.93 97.98
60.25 96.41
62.56 97.25
64.88 95.99
67.2 93.4
69.51 93.39
71.83 92.72
74.15 93.38
76.47 92.9
78.78 91.85
81.1 90.7
83.42 90.2
85.73 88.6
88.05 88.31
90.37 88.17
92.69 87.91
95 88.04
97.32 88.04
99.64 88.88
101.95 90.28
104.27 89.88
106.59 90.29
108.91 90.24
111.22 90.31
113.54 89.84
115.86 89.49