AC5 (ac_5)

Race #457

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Official speed 80.59 wpm (128.65 seconds elapsed during race)
Without ending ping 80.67 wpm (124 ms delay sending score to TypeRacer’s server)
Timerless 80.94 wpm (428 ms elapsed before first character typed; 128.10 seconds elapsed during race)
Timerless minus one 80.84 wpm, ignoring the first character typed
Race Start September 25, 2023 1:11:31am UTC
Race Finish September 25, 2023 1:13:40am UTC
Outcome Win (1 of 4)
Opponents 3. koppix (75.35 wpm)
Accuracy 97.4%
Points 217.59
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 tollol that helps us unsderstand how a change in one quantity is related to a change in another. How does the speed of a falling iobject change as a function of time? How does the level of water in a barrlele le el change as a function of the amoutn of nt of liquid poured into it? We see change occuring ring in nearly evertyyything we observe in the world and universe, and powerful modern instruments helkp p us see more and mroeore. In this ecsection we interoroduce the ideas of average and instantaneous rates of change, and show that they are closely lrealterelated to the slop of e of a cuvrve at a Ppoint P on the curve. We fgive precise developments of these important concepts in the nest xt chapter, but for now we use an informal apporacraooach 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 throguughout calculus.
Timing
Character C a l c u l u s i s a t o l l -l -l o l t h
Milliseconds 428 150 119 515 100 118 200 158 67 105 131 56 123 44 146 86 147 212 339 155 239 175 216 73 63
Character a t h e l p s u s u n s -s d e r s t a n d
Milliseconds 135 40 57 189 83 119 16 138 105 49 146 39 148 86 349 283 33 91 145 156 99 195 154 105 44
Character h o w a c h a n g e i n o n e q u a n t
Milliseconds 267 60 142 52 255 50 163 81 118 87 132 0 94 53 109 174 87 196 132 44 135 136 159 108 107
Character i t y i s r e l a t e d t o a c h a n g
Milliseconds 85 130 171 226 174 159 65 171 40 138 18 143 39 175 96 146 75 104 130 42 141 62 68 140 129
Character e i n a n o t h e r . H o w d o e s t h
Milliseconds 25 104 43 126 142 42 116 55 95 112 50 102 56 179 201 163 134 115 134 60 73 167 126 68 112
Character e s p e e d o f a f a l l i n g i -i o b
Milliseconds 83 34 153 99 109 150 96 127 52 133 67 138 52 191 103 155 159 123 117 63 114 214 430 223 121
Character j e c t c h a n g e a s a f u n c t i o n
Milliseconds 608 73 101 306 110 91 113 88 116 103 31 95 118 79 32 180 33 243 45 66 123 157 105 92 62
Character o f t i m e ? H o w d o e s t h e l e
Milliseconds 202 204 75 99 123 56 84 72 285 188 215 184 152 41 131 58 128 166 56 65 123 43 102 156 0
Character v e l o f w a t e r i n a b a r r l e -e
Milliseconds 184 71 324 240 60 187 37 135 160 51 138 89 36 210 106 166 101 308 186 130 141 164 123 48 274
Character -l l e - -e -l l e - -e -l e l c h a n g e a s
Milliseconds 131 133 11 202 314 143 175 149 50 260 245 175 184 278 157 195 83 139 0 135 134 0 152 110 62
Character a f u n c t i o n o f t h e a m o u t n
Milliseconds 31 194 0 260 39 84 45 199 0 121 103 168 79 120 80 130 73 70 75 118 84 94 92 126 0
Character o f - -f -o - -n -t n t o f l i q u i d p o
Milliseconds 88 43 87 93 419 165 171 145 100 164 216 93 131 95 124 137 98 182 179 438 125 233 141 213 210
Character u r e d i n t o i t ? W e s e e c h a n
Milliseconds 260 84 211 109 104 93 89 77 87 104 234 155 406 171 264 228 114 89 164 192 135 100 123 100 72
Character g e o c c u r i n g - -g -n -i r i n g i n n
Milliseconds 140 0 43 205 118 170 146 96 110 38 104 123 471 157 139 120 201 74 129 94 59 146 60 176 143
Character e a r l y e v e r t y -y y -y -t y t h i n g w e
Milliseconds 48 149 37 159 37 162 148 100 111 158 274 0 361 88 116 183 195 200 41 59 166 42 137 106 93
Character o b s e r v e i n t h e w o r l d a n d
Milliseconds 77 165 127 196 156 100 219 40 77 112 104 172 68 115 50 108 107 114 98 274 165 129 107 129 56
Character u n i v e r s e , a n d p o w e r f u l m
Milliseconds 65 150 48 191 81 149 589 175 155 226 180 83 133 48 83 102 91 106 37 172 180 38 119 142 248
Character o d e r n i n s t r u m e n t s h e l k p -
Milliseconds 141 75 147 36 322 208 134 89 92 183 54 99 176 97 104 108 100 102 271 168 93 35 0 274 222
Character -p -k p u s s e e m o r e a n d m r o e -e
Milliseconds 167 168 225 184 128 134 350 169 149 153 87 159 78 58 79 55 140 108 71 92 157 96 0 34 550
Character -o -r o r e . I n t h i s e c -c -e s e c t i o
Milliseconds 168 149 364 170 41 166 264 124 232 178 66 139 35 108 94 95 199 297 149 114 220 0 190 65 83
Character n w e i n t e r o -o -r -e r o d u c e t h e
Milliseconds 104 272 51 93 54 147 109 39 111 0 116 268 154 145 194 80 182 92 142 166 67 188 42 109 88
Character i d e a s o f a v e r a g e a n d i n s t
Milliseconds 80 93 42 138 112 108 72 187 40 137 151 98 81 141 94 148 0 118 157 92 55 139 81 75 73
Character a n t a n e o u s r a t e s o f c h a n g e
Milliseconds 93 90 125 182 102 453 154 70 177 65 145 104 98 40 190 128 115 167 63 138 73 327 293 186 14
Character , a n d s h o w t h a t t h e y a r e
Milliseconds 479 217 72 74 122 53 149 52 76 127 74 240 95 101 63 74 158 42 146 52 126 108 48 58 86
Character c l o s e l y l r e a l t e -l -r -e -a -l -t -e r e l
Milliseconds 143 47 214 37 171 130 142 91 116 60 38 139 101 123 0 332 0 0 0 0 0 0 444 36 181
Character a t e d t o t h e s l o p o f - -f -o - e
Milliseconds 54 130 39 180 51 150 35 161 65 140 110 46 168 61 214 93 209 82 129 108 258 170 148 182 207
Character o f a c u v -v r v e a t a P -P p o i n
Milliseconds 106 176 91 69 111 62 205 110 134 244 65 216 41 94 155 78 71 113 59 289 472 217 180 284 90
Character t P o n t h e c u r v e . W e f -f g i
Milliseconds 150 49 207 179 119 95 144 98 57 114 97 78 160 11 246 46 177 536 259 361 94 163 296 137 87
Character v e p r e c i s e d e v e l o p m e n t s o
Milliseconds 109 72 42 165 107 45 227 170 163 163 40 227 86 288 44 101 96 37 230 103 115 91 102 94 97
Character f t h e s e i m p o r t a n t c o n c e p t
Milliseconds 139 53 142 43 96 186 124 44 175 99 86 115 42 145 102 152 133 170 242 157 152 26 70 85 124
Character s i n t h e n e s t - -t -s x t c h a p t
Milliseconds 133 138 28 137 162 91 97 122 105 290 47 198 92 95 318 161 438 82 172 118 389 124 112 42 182
Character e r , b u t f o r n o w w e u s e a n
Milliseconds 102 91 179 189 197 303 154 45 182 102 116 41 189 61 60 100 165 117 105 320 172 105 151 172 154
Character i n f o r m a l a p p o r a c -c -a -r -o r a o -o
Milliseconds 189 164 86 119 99 180 181 162 67 108 151 83 172 112 38 160 92 277 155 147 163 265 401 388 127
Character -a o a c h s o y o u w i l l s e e h o w
Milliseconds 232 186 101 47 94 175 96 107 139 162 96 48 151 102 99 43 168 107 244 175 128 35 213 17 86
Character t h e y l e a d n a t u r a l l y t o t
Milliseconds 133 61 107 99 59 137 131 107 123 35 39 162 47 92 103 75 160 19 161 147 234 358 51 137 358
Character h e m a i n i d e a o f t h i s c h a p
Milliseconds 55 143 84 168 56 145 54 183 107 68 67 95 159 32 363 134 119 103 55 41 152 83 62 48 106
Character t e r , t h e l i m i t . T h e i d e a
Milliseconds 137 121 57 136 101 93 64 91 102 113 104 39 154 77 166 191 166 148 106 115 61 93 42 120 123
Character o f a l i m i t p l a y s a f o u n d a
Milliseconds 147 99 72 126 61 124 134 68 158 30 161 41 86 106 160 119 19 445 556 173 87 48 149 182 142
Character t i o n a l r o l e t h r o g u -u -g u g h o u
Milliseconds 91 87 62 99 108 123 112 179 93 174 49 110 101 105 103 41 227 28 326 152 215 97 120 116 60
Character t c a l c u l u s .
Milliseconds 110 39 172 97 30 192 67 102 188 161 121
WPM Timing
Seconds WPM
2.57 74.62
5.15 72.29
7.72 74.62
10.29 81.62
12.87 86.75
15.44 90.94
18.01 93.28
20.58 88.03
23.16 90.68
25.73 90.94
28.3 90.73
30.88 83.17
33.45 85.02
36.02 82.95
38.6 81.46
41.17 81.03
43.74 81.48
46.31 80.58
48.89 79.28
51.46 80.22
54.03 79.95
56.61 80.77
59.18 80.3
61.75 80.26
64.33 78.72
66.9 78.75
69.47 78.42
72.04 79.95
74.62 80.25
77.19 80.06
79.76 80.64
82.34 80.6
84.91 79.57
87.48 78.87
90.06 79.15
92.63 78.64
95.2 79.28
97.77 79.78
100.35 79.04
102.92 78.93
105.49 79.17
108.07 78.51
110.64 77.87
113.21 78.54
115.79 78.77
118.36 79.49
120.93 80.18
123.51 80.26
126.08 80.71
128.65 80.59