#5_Semesters (supeer_heroo)

Race #6732

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Official speed 80.51 wpm (128.78 seconds elapsed during race)
Without ending ping 80.69 wpm (292 ms delay sending score to TypeRacer’s server)
Timerless 80.95 wpm (410 ms elapsed before first character typed; 128.08 seconds elapsed during race)
Timerless minus one 80.86 wpm, ignoring the first character typed
Race Start December 30, 2023 9:18:47pm UTC
Race Finish December 30, 2023 9:20:56pm UTC
Outcome Win (1 of 3)
Accuracy 96.6%
Points 217.38
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 u s 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 fucnction of time? How does the level of water in a barrel change as a function of the amou nt of liquid puoroured into it? We see change occuring ring in renearly everything we observei n i in the world and universe, and powerful modern instrument s hoelpu ujss see more and more. In this section we introducew th the ideas of average and instantaneous reatats es of change, and show that they aeare dlclsoeoeslsely related oto the slope of a curve ata a point P on the ucurve. wWe give predicise developemments of these important concepts in the next chapter, tbut for now we use an infromaoormal approach so you will see how they lead naturally to ghthe main idea of this chapter, the limit. The ieadea of a mlimtit 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 410 113 71 217 327 190 210 422 115 103 384 97 121 172 330 30 142 192 106 83 119 0 114 54 103
Character e l p s u - s u n d e r s t a n d h o w
Milliseconds 137 78 191 112 96 102 170 383 64 101 87 175 75 163 75 253 119 141 103 146 72 106 110 62 115
Character a c h a n g e i n o n e q u a n t i t y
Milliseconds 81 109 237 50 233 108 146 91 80 82 109 78 74 119 25 107 263 77 130 139 212 325 147 98 92
Character i s r e l a t e d t o a c h a n g e i n
Milliseconds 163 96 93 180 80 386 85 166 64 184 78 223 92 105 64 150 159 82 85 94 110 73 52 133 70
Character a n o t h e r . H o w d o e s t h e s p
Milliseconds 120 133 92 130 95 88 79 81 68 87 196 64 126 89 111 73 91 95 70 156 79 109 30 205 93
Character e e d o f a f a l l i n g o b j e c t c
Milliseconds 86 160 190 71 123 73 99 76 95 165 128 119 163 129 181 148 91 184 166 196 57 195 180 72 332
Character h a n g e a s a f u c -c n c t i o n o f
Milliseconds 131 0 154 93 95 122 131 120 83 117 82 146 99 174 357 154 51 198 26 98 77 91 87 86 54
Character t i m e ? H o w d o e s t h e l e v e l
Milliseconds 183 88 51 57 264 111 162 81 84 114 90 93 82 87 84 107 74 90 60 103 104 145 276 115 189
Character o f w a t e r i n a b a r r e l c h a n
Milliseconds 71 141 36 176 90 139 81 105 64 93 81 100 71 120 127 124 160 149 69 111 138 162 82 24 163
Character g e a s a f u n c t i o n o f t h e a
Milliseconds 102 47 104 164 109 92 101 111 81 146 200 184 200 30 118 45 114 104 96 78 97 38 110 55 250
Character m o u - n t o f l i q u i d p u o r -r -o -u
Milliseconds 103 95 121 256 373 159 113 69 111 131 52 171 108 214 337 150 207 131 454 161 0 278 166 147 133
Character o u r e d i n t o i t ? W e s e e c h a
Milliseconds 163 74 89 97 156 67 111 83 120 51 118 75 92 253 135 215 195 130 66 176 162 82 150 53 115
Character n g e o c c u r i n g - -g -n -i r i n g i n
Milliseconds 86 116 90 44 211 138 147 126 138 75 104 90 67 269 141 162 129 105 96 64 114 50 75 80 121
Character r e -e -r n e a r l y e v e r y t h i n g w e
Milliseconds 193 37 283 143 182 56 73 64 66 140 105 208 115 103 118 59 181 53 134 82 97 84 84 58 128
Character o b s e r v e i n -n - i -i - -i i n t h e
Milliseconds 227 127 190 126 157 241 46 144 133 106 258 132 153 108 272 132 165 319 147 82 126 66 73 65 100
Character w o r l d a n d u n i v e r s e , a n d p
Milliseconds 69 72 88 86 121 54 157 53 125 53 148 192 72 119 91 148 136 71 134 85 50 121 61 95 104
Character o w e r f u l m o d e r n i n s t r u m e n t
Milliseconds 114 90 48 136 133 45 117 147 124 115 58 178 79 154 60 129 108 20 187 200 106 196 59 130 53
Character - s h o -o e l p u -u u j s -s -j s s e e m
Milliseconds 147 308 101 171 148 158 410 165 77 183 186 413 161 117 0 40 379 158 150 31 417 176 155 69 128
Character o r e a n d m o r e . I n t h i s s e c
Milliseconds 64 79 44 69 122 54 126 90 218 86 73 39 125 90 173 82 125 90 32 84 101 47 128 125 241
Character t i o n w e i n t r o d u c e w t h -h -t - -w
Milliseconds 200 55 97 58 132 92 39 140 117 72 153 200 72 394 108 82 153 0 100 86 94 220 140 175 151
Character t h e i d e a s o f a v e r a g e a n d
Milliseconds 136 43 93 68 93 118 82 152 98 145 96 130 94 78 155 144 102 290 120 125 76 98 124 82 85
Character i n s t a n t a n e o u s r e a t -t -a -e a t s
Milliseconds 85 80 93 45 179 193 211 163 340 595 118 267 82 209 113 178 75 107 122 282 136 156 112 108 141
Character - -s e s o f c h a n g e , a n d s h o w
Milliseconds 167 284 137 198 195 126 127 68 106 146 82 28 180 75 71 101 101 51 106 68 122 181 87 115 162
Character t h a t t h e y a e -e -a a r e d l -l -d c l
Milliseconds 108 117 98 43 101 41 181 34 207 84 213 188 135 362 135 452 96 75 102 187 91 295 126 88 109
Character s o e -e -o -s o e s l -l -s -e s e l y r e l a t e d
Milliseconds 142 21 157 218 129 144 165 82 100 103 300 130 151 225 66 97 185 91 140 106 315 121 185 58 195
Character o -o t o t h e s l o p e o f a c u r v
Milliseconds 67 140 437 338 78 110 50 124 35 117 197 79 174 149 170 186 71 111 101 77 109 129 132 93 203
Character e a t a - -a a p o i n t P o n t h e
Milliseconds 38 123 63 121 145 109 305 140 124 100 108 169 122 109 113 70 131 299 182 211 103 145 30 136 53
Character u -u c u r v e . w -w W e g i v e p r e d i
Milliseconds 95 257 424 85 127 151 253 68 98 96 272 440 276 193 190 88 83 160 54 119 142 101 231 246 137
Character -i -d c i s e d e v e l o p e m -m -e m e n t s o
Milliseconds 319 147 87 119 70 72 125 112 149 174 0 493 180 133 239 38 259 131 135 87 103 131 265 135 62
Character f t h e s e i m p o r t a n t c o n c e p t
Milliseconds 126 65 108 20 118 171 64 161 107 124 86 157 108 497 156 61 165 124 145 55 66 246 163 79 81
Character s i n t h e n e x t c h a p t e r , t -t
Milliseconds 136 108 103 88 86 69 75 49 86 94 173 237 199 128 236 100 52 262 105 116 136 131 137 115 305
Character b u t f o r n o w w e u s e a n i n f
Milliseconds 69 73 111 52 138 68 114 149 166 87 118 110 140 80 97 110 107 57 97 91 95 97 158 120 147
Character r o m a -a -m -o o -o -r o r m a l a p p r o a c h
Milliseconds 151 37 143 96 253 128 165 161 293 136 142 90 200 129 107 138 132 117 121 92 98 371 284 155 125
Character s o y o u w i l l s e e h o w t h e y
Milliseconds 145 190 105 107 75 88 67 74 78 151 148 93 91 122 68 124 453 125 326 141 82 75 112 68 77
Character l e a d n a t u r a l l y t o g h -h -g t h e
Milliseconds 103 53 76 145 57 178 50 165 92 170 114 103 155 86 93 146 55 96 100 138 240 132 83 80 70
Character m a i n i d e a o f t h i s c h a p t e
Milliseconds 70 152 111 80 126 79 134 35 142 75 137 91 127 54 149 54 81 91 57 147 78 68 128 88 108
Character r , t h e l i m i t . T h e i e a -a -e d e
Milliseconds 111 90 119 79 69 98 51 142 83 243 233 165 161 93 150 107 56 108 196 58 68 313 128 26 165
Character a o f a m -m l i m t -t i t p l a y s a
Milliseconds 90 95 85 130 106 95 69 514 303 172 99 96 163 504 150 86 105 139 162 254 161 203 142 76 114
Character f o u n d a t i o n a l r o l e t h r o u g h
Milliseconds 214 113 22 184 83 128 159 338 141 86 89 101 135 160 75 165 119 89 122 39 139 35 58 112 59
Character o u t c a l c u l u s .
Milliseconds 107 82 49 107 204 91 90 130 127 134 194 147 67
WPM Timing
Seconds WPM
2.58 51.25
5.15 72.22
7.73 77.65
10.3 80.37
12.88 82
15.45 88.52
18.03 91.19
20.6 90.27
23.18 90.59
25.76 92.72
28.33 94.45
30.91 95.12
33.48 92.82
36.06 90.19
38.63 90.7
41.21 88.81
43.78 89.07
46.36 86.19
48.94 86.81
51.51 88.29
54.09 87.41
56.66 84.92
59.24 86.3
61.81 86.58
64.39 85.91
66.97 86.19
69.54 84.38
72.12 83.86
74.69 84.19
77.27 82.31
79.84 81.01
82.42 80.66
84.99 80.48
87.57 80.58
90.15 79.6
92.72 79.33
95.3 78.7
97.87 79.08
100.45 79.44
103.02 79.67
105.6 79.32
108.17 78.87
110.75 79.21
113.33 79.84
115.9 80.14
118.48 80.72
121.05 80.49
123.63 79.79
126.2 80.06
128.78 80.51