Karsten (dutchie3)

Race #6894

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Official speed 79.93 wpm (129.71 seconds elapsed during race)
Without ending ping 80.13 wpm (328 ms delay sending score to TypeRacer’s server)
Timerless 80.93 wpm (1,280 ms elapsed before first character typed; 128.11 seconds elapsed during race)
Timerless minus one 80.84 wpm, ignoring the first character typed
Race Start January 1, 2024 6:10:51pm UTC
Race Finish January 1, 2024 6:13:01pm UTC
Outcome No win (4 of 5)
Accuracy 97.1%
Points 215.81
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 tooll that helps us understand how a change in one quantity is related to a change in oanother. How does the speed of a falling object change a s a function of time? How does the level of water ina a a barrle el achange as a function fofof the amount o f liquid poured into it? Wee see change occuring ring in nearly everything we observe in the world and universe, and powerful modern insturuments hel; p us see more and more. In this esection we introduce the ideas of average and instatntaneous rater ofss of change, and show that they are closleely related to the slope of a curve at a pontint P onth the cuvrve. We give perecise development s of these important concepts in the next chapter, but for now we use an infomrmal aapporroach so you will see how they lead naaturally to the main idea of this chapter, the limit. The idea of a litmit plays a foundationsal role throughout calculus.
Timing
Character C a l c u l u s i s a t o o l l - -l t h
Milliseconds 1280 215 111 199 74 167 167 243 88 62 349 86 140 107 137 101 156 11 79 148 357 116 84 97 68
Character a t h e l p s u s u n d e r s t a n d h o
Milliseconds 109 50 81 133 76 135 219 127 82 137 71 104 120 135 47 155 115 128 136 52 68 136 124 102 52
Character w a c h a n g e i n o n e q u a n t i t
Milliseconds 82 96 260 116 235 98 100 94 129 111 102 89 50 124 110 57 120 100 264 85 450 114 126 111 109
Character y i s r e l a t e d t o a c h a n g e
Milliseconds 183 121 136 458 100 114 99 118 119 126 162 167 112 48 111 92 333 162 144 93 109 70 186 94 100
Character i n o -o a n o t h e r . H o w d o e s t h
Milliseconds 42 79 102 114 331 307 110 59 91 97 41 107 140 112 259 91 78 94 124 97 115 91 98 131 77
Character e s p e e d o f a f a l l i n g o b j e
Milliseconds 71 104 162 53 128 115 190 85 96 100 100 124 151 286 70 86 135 47 64 75 30 118 128 147 87
Character c t c h a n g e a - s a f u n c t i o n
Milliseconds 183 121 44 229 90 107 86 64 151 110 206 131 462 47 89 110 129 97 93 130 99 133 35 61 27
Character o f t i m e ? H o w d o e s t h e l e
Milliseconds 120 87 92 79 135 52 68 48 328 90 240 68 402 103 213 57 134 67 89 77 68 73 102 195 111
Character v e l o f w a t e r i n a a -a - -a a b
Milliseconds 168 64 125 132 133 111 105 384 85 130 109 82 67 43 75 126 140 134 271 145 149 150 140 336 197
Character a r r l e - -e -l e l a -a c h a n g e a s a
Milliseconds 174 182 131 145 91 82 382 136 149 75 115 97 89 397 128 130 105 94 103 58 97 127 480 88 110
Character f u n c t i o n f o f -f -o -f o f t h e a m
Milliseconds 134 119 129 120 79 113 39 61 25 144 65 19 149 291 143 130 193 55 96 112 52 63 86 151 118
Character o u n t o - f l i q u i d p o u r e d i
Milliseconds 129 51 148 298 104 145 157 410 100 77 220 136 250 154 62 271 262 222 245 78 118 233 174 35 104
Character n t o i t ? W e e - -e s e e c h a n g e
Milliseconds 51 223 285 106 150 96 284 108 195 111 103 115 348 98 78 78 114 153 97 154 158 93 133 92 92
Character o c c u r i n g - -g -n -i r i n g i n n e a
Milliseconds 107 129 245 165 81 111 91 74 79 93 291 129 146 124 103 95 38 108 51 59 73 127 97 66 104
Character r l y e v e r y t h i n g w e o b s e r v e
Milliseconds 9 162 150 70 235 156 60 101 86 112 68 61 80 69 89 149 89 142 152 138 347 80 104 233 79
Character i n t h e w o r l d a n d u n i v e r s
Milliseconds 150 65 69 119 42 99 26 113 83 93 73 93 113 111 78 70 116 75 77 139 89 110 170 370 177
Character e , a n d p o w e r f u l m o d e r n i n
Milliseconds 216 108 108 99 80 86 65 116 111 106 88 123 178 96 105 108 145 95 88 182 53 128 115 168 102
Character s t u -u r u m e n t s h e l ; - -; p u s s
Milliseconds 90 105 145 346 126 106 146 99 92 138 285 62 151 66 119 117 192 345 111 200 76 102 89 93 283
Character e e m o r e a n d m o r e . I n t h i s
Milliseconds 93 190 75 122 40 102 95 81 198 103 91 73 48 71 89 53 215 72 200 81 105 109 69 43 72
Character e -e s e c t i o n w e i n t r o d u c e t
Milliseconds 110 132 385 74 94 209 171 88 48 47 110 139 143 135 108 43 106 190 385 385 72 135 166 122 107
Character h e i d e a s o f a v e r a g e a n d i
Milliseconds 87 54 134 359 112 146 112 171 79 46 1228 84 102 459 130 74 138 158 65 97 424 111 89 89 82
Character n s t a t -t n t a n e o u s r a t e r o f -f -o
Milliseconds 80 184 128 273 127 424 198 151 167 264 151 293 153 249 165 266 108 175 116 93 122 51 108 328 149
Character - s -s -r s o f c h a n g e , a n d s h o w
Milliseconds 308 32 223 166 90 66 159 104 102 320 99 144 53 180 66 83 100 77 78 74 108 122 104 69 77
Character t h a t t h e y a r e c l o s l e -e -l e l
Milliseconds 136 120 60 47 111 44 135 69 122 81 109 112 115 55 99 195 133 449 426 134 146 374 96 78 111
Character y r e l a t e d t o t h e s l o p e o f
Milliseconds 151 104 89 114 67 173 90 82 186 117 20 119 87 84 70 44 73 86 102 186 95 120 119 128 80
Character a c u r v e a t a p o n t -t -n i n t P
Milliseconds 72 193 147 572 78 99 240 86 107 102 220 91 137 135 107 42 181 77 408 131 184 65 71 97 221
Character o n t h -h -t t h e c u v -v r v e . W e g
Milliseconds 209 113 108 205 96 324 111 119 124 73 99 49 147 45 303 339 108 211 105 137 96 430 179 106 132
Character i v e p e -e r e c i s e d e v e l o p m e n t
Milliseconds 33 181 51 124 106 88 344 169 70 243 85 129 172 120 126 188 187 43 168 155 73 178 70 101 102
Character - s o f t h e s e i m p o r t a n t c o
Milliseconds 121 328 85 65 171 79 80 99 78 159 101 148 19 70 176 597 78 110 160 111 120 147 78 151 107
Character n c e p t s i n t h e n e x t c h a p t e
Milliseconds 56 227 174 98 132 258 89 88 41 107 130 34 108 80 22 113 214 192 154 235 275 118 130 201 108
Character r , b u t f o r n o w w e u s e a n
Milliseconds 121 131 113 125 37 133 99 107 48 111 83 283 92 107 87 153 143 107 170 73 88 130 189 110 127
Character i n f o m -m r m a l a a -a p p o r -r -o r o a c h
Milliseconds 82 49 141 126 74 475 88 113 145 52 125 258 201 490 299 151 104 83 388 105 134 109 101 187 185
Character s o y o u w i l l s e e h o w t h e y
Milliseconds 118 173 31 162 143 33 80 69 61 85 156 110 59 100 113 174 93 87 57 66 96 169 76 82 77
Character l e a d n a a -a t u r a l l y t o t h e
Milliseconds 78 84 65 82 175 98 199 96 103 443 87 113 151 186 162 136 150 105 104 81 116 132 40 102 56
Character m a i n i d e a o f t h i s c h a p t e r
Milliseconds 95 109 62 82 57 124 85 151 75 134 61 122 54 124 54 273 121 87 224 98 129 73 371 129 110
Character , t h e l i m i t . T h e i d e a o f
Milliseconds 145 107 126 25 106 81 37 75 128 150 137 143 106 208 144 77 60 251 544 175 88 114 105 43 124
Character a l i t -t m i t p l a y s a f o u n d a t
Milliseconds 349 106 119 43 202 362 180 97 94 144 118 164 89 99 128 85 113 118 212 218 60 154 93 113 92
Character i o n s -s a l r o l e t h r o u g h o u t c
Milliseconds 39 50 54 174 452 83 127 85 164 43 198 61 99 228 439 144 85 38 858 157 127 54 101 87 192
Character a l c u l u s .
Milliseconds 130 21 347 103 122 160 186 97
WPM Timing
Seconds WPM
2.59 41.63
5.19 60.13
7.78 75.55
10.38 78.63
12.97 80.49
15.57 80.18
18.16 83.92
20.75 86.73
23.35 87.37
25.94 87.89
28.54 87.04
31.13 82.49
33.73 81.84
36.32 81.94
38.91 80.49
41.51 79.79
44.1 79.72
46.7 79.41
49.29 80.34
51.89 82.34
54.48 82.82
57.07 82.63
59.67 82.25
62.26 82.87
64.86 82.71
67.45 81.84
70.05 81.72
72.64 80.45
75.23 78.79
77.83 80.02
80.42 79.38
83.02 80.22
85.61 80.18
88.21 79.32
90.8 78.63
93.39 78.63
95.99 78.88
98.58 79
101.18 79.23
103.77 79.79
106.37 79.54
108.96 78.74
111.55 79.71
114.15 79.69
116.74 80.38
119.34 80.75
121.93 80.21
124.52 80.56
127.12 80.15
129.71 79.93