Ghafass (ghafass)

Race #3014

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Official speed 78.31 wpm (132.40 seconds elapsed during race)
Without ending ping 79.13 wpm (1,374 ms delay sending score to TypeRacer’s server)
Timerless 79.35 wpm (366 ms elapsed before first character typed; 130.66 seconds elapsed during race)
Timerless minus one 79.26 wpm, ignoring the first character typed
Race Start November 18, 2024 4:11:17pm UTC
Race Finish November 18, 2024 4:13:29pm UTC
Outcome Win (1 of 3)
Opponents 2. egovangel (73.30 wpm)
Accuracy 97.7%
Points 211.44
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 Calcculus is a tool that helps us understand how a change in one qunatantity is related to a change in another. Hows do does the speed of a falling object change a s a function of tiemme? How does the level of water in a barrel change as a function of the amount of liquid poured into it? We see change occruuringring. in nearly everything we observe in the world and universe, and powerful modern instrum\entents help us esee more and more. In thiss e section we introduce the ideas of average and instantaneous raates of chagnge, and show that they are clsoosely reltaated to the slope of a cruvurve at a point P on the curve. We give precise developments of thse ese important concepts in the next chapter, but for now we use an informal approach so you will see how they lead natualrally to the main idea of this chapter, the limit. The idea of a ilimit plays a foundational role throughout calculus.
Timing
Character C a l c c -c u l u s i s a t o o l t h a t
Milliseconds 366 214 128 79 494 455 235 188 155 100 133 183 106 112 82 98 99 102 180 186 154 113 116 51 67
Character h e l p s u s u n d e r s t a n d h o w
Milliseconds 82 185 51 196 35 163 137 141 100 100 179 59 68 41 144 189 132 79 113 76 133 192 175 93 133
Character a c h a n g e i n o n e q u n a t -t -a -n a
Milliseconds 53 148 99 119 37 165 113 53 101 166 361 186 188 59 119 90 222 123 502 113 165 336 179 141 68
Character n t i t y i s r e l a t e d t o a c h a
Milliseconds 167 111 67 127 106 233 168 79 114 74 61 119 65 115 85 156 68 188 89 213 88 113 88 126 266
Character n g e i n a n o t h e r . H o w s d o -o -d
Milliseconds 234 101 67 108 191 52 221 96 85 167 65 100 82 46 199 230 223 168 80 191 77 117 100 373 178
Character - -s d o e s t h e s p e e d o f a f a
Milliseconds 185 133 222 67 112 68 176 68 121 112 89 159 119 134 81 174 59 85 166 57 225 176 99 78 100
Character l l i n g o b j e c t c h a n g e a - s
Milliseconds 200 167 134 59 63 139 152 180 119 56 78 238 123 289 108 65 145 55 78 135 127 164 459 63 200
Character a f u n c t i o n o f t i e m -m -e m e ? H
Milliseconds 83 182 157 135 65 34 234 33 45 233 178 167 133 117 133 51 122 100 449 152 247 132 256 233 222
Character o w d o e s t h e l e v e l o f w a t e
Milliseconds 178 72 172 81 119 47 176 79 124 102 51 166 181 21 88 100 100 211 182 90 118 227 51 268 113
Character r i n a b a r r e l c h a n g e a s a
Milliseconds 87 93 165 42 201 128 116 167 82 118 213 70 135 183 123 100 67 144 80 36 130 189 66 112 89
Character f u n c t i o n o f t h e a m o u n t o
Milliseconds 101 126 106 60 141 200 34 44 223 211 189 64 143 52 142 57 143 145 67 193 52 221 82 116 155
Character f l i q u i d p o u r e d i n t o i t ?
Milliseconds 76 132 220 60 162 178 80 279 219 382 219 56 100 68 188 10 200 45 133 89 199 160 51 304 230
Character W e s e e c h a n g e o c c r u -u -r u r i n
Milliseconds 149 186 115 118 179 353 160 97 123 23 191 42 46 132 189 65 226 319 117 384 156 212 100 100 82
Character g -g -n -i r i n g . - -. i n n e a r l y e v
Milliseconds 96 325 163 169 79 214 39 146 288 212 353 152 213 172 58 212 186 83 73 146 54 232 236 44 117
Character e r y t h i n g w e o b s e r v e i n t h
Milliseconds 134 98 109 158 100 66 147 53 165 135 179 88 188 169 75 191 93 231 68 153 194 67 184 134 122
Character e w o r l d a n d u n i v e r s e , a n d
Milliseconds 47 180 65 142 112 114 74 145 100 115 167 68 241 21 223 56 166 84 196 133 93 197 43 167 104
Character p o w e r f u l m o d e r n i n s t r u m \
Milliseconds 89 200 67 35 205 78 291 91 100 274 189 112 90 80 141 94 199 166 68 86 188 101 191 241 40
Character e n t -t -n -e -\ e n t s h e l p u s e -e s e e
Milliseconds 0 167 26 350 159 178 146 0 179 20 167 94 199 101 165 69 274 189 111 125 88 401 67 166 160
Character m o r e a n d m o r e . I n t h i s s
Milliseconds 88 188 59 99 66 120 56 144 80 114 203 31 73 68 246 232 279 226 198 80 149 33 65 189 0
Character e -e - -s s e c t i o n w e i n t r o d u c e
Milliseconds 245 285 181 142 212 56 188 145 227 20 43 248 176 66 250 76 341 67 105 62 166 147 167 127 67
Character t h e i d e a s o f a v e r a g e a n d
Milliseconds 206 234 59 108 144 169 43 186 52 212 108 166 112 133 50 173 192 59 183 201 57 123 100 113 99
Character i n s t a n t a n e o u s r a a -a t e s o f
Milliseconds 88 166 67 128 332 198 121 89 773 100 175 265 80 116 140 259 74 201 378 61 52 188 128 173 78
Character c h a g -g n g e , a n d s h o w t h a t
Milliseconds 115 85 133 18 306 406 200 74 44 89 167 77 182 102 134 107 99 144 68 167 89 133 12 92 129
Character t h e y a r e c l s o -o -s o s e l y r e l t
Milliseconds 79 127 52 115 218 48 107 94 99 169 107 188 24 444 148 200 29 172 67 270 285 146 72 67 126
Character a -a -t a t e d t o t h e s l o p e o f a
Milliseconds 134 399 167 375 159 85 146 121 134 80 214 68 118 55 160 74 127 198 35 118 181 200 108 128 51
Character c r u v -v -u -r u r v e a t a p o i n t P
Milliseconds 163 38 194 35 183 373 183 134 202 57 197 70 120 127 169 136 83 164 200 183 40 226 53 156 206
Character o n t h e c u r v e . W e g i v e p r
Milliseconds 199 151 68 198 49 142 34 177 49 141 92 219 50 140 200 155 189 134 113 123 90 74 79 189 61
Character e c i s e d e v e l o p m e n t s o f t h s
Milliseconds 53 189 96 178 167 102 180 52 188 50 150 192 87 266 100 191 65 208 93 179 46 142 78 133 82
Character e - -e -s e s e i m p o r t a n t c o n c e p
Milliseconds 178 108 367 178 158 39 160 167 91 232 221 202 67 79 199 101 155 79 151 149 66 48 114 85 68
Character t s i n t h e n e x t c h a p t e r , b
Milliseconds 146 185 48 171 63 185 118 115 84 140 178 23 225 734 254 101 177 68 244 138 152 89 33 204 163
Character u t f o r n o w w e u s e a n i n f o
Milliseconds 64 94 122 111 89 127 74 348 78 119 166 35 211 122 178 57 166 46 132 102 188 179 57 75 124
Character r m a l a p p r o a c h s o y o u w i l l
Milliseconds 92 100 81 135 182 101 115 133 107 102 17 160 83 206 127 74 167 233 93 86 211 101 91 176 155
Character s e e h o w t h e y l e a d n a t u a l
Milliseconds 181 80 165 153 96 198 35 85 154 94 106 47 146 208 170 109 55 144 91 199 74 94 166 81 143
Character -l -a r a l l y t o t h e m a i n i d e a
Milliseconds 455 177 84 20 153 133 211 223 135 46 199 66 121 78 146 166 69 142 57 201 153 45 214 31 139
Character o f t h i s c h a p t e r , t h e l i m i
Milliseconds 182 89 128 73 134 32 68 145 84 131 51 133 83 134 73 68 189 69 152 28 173 267 213 167 189
Character t . T h e i d e a o f a i -i l i m i t
Milliseconds 93 205 213 124 109 66 135 148 56 185 47 191 207 120 114 137 96 246 333 249 207 167 191 82 119
Character p l a y s a f o u n d a t i o n a l r o l e
Milliseconds 185 33 67 212 156 185 115 113 523 44 33 221 67 45 282 21 81 183 67 114 188 95 106 178 58
Character t h r o u g h o u t c a l c u l u s .
Milliseconds 131 78 122 100 99 68 166 14 254 33 112 155 283 132 97 195 108 411 223 92 165
WPM Timing
Seconds WPM
2.65 40.79
5.3 72.51
7.94 83.08
10.59 74.78
13.24 77.04
15.89 80.06
18.54 74.45
21.18 77.04
23.83 78.05
26.48 78.4
29.13 75.81
31.78 77.8
34.42 79.48
37.07 80.93
39.72 80.67
42.37 80.44
45.01 79.17
47.66 76.03
50.31 77.04
52.96 77.72
55.61 78.55
58.25 79.1
60.9 78.03
63.55 77.99
66.2 77.4
68.85 77.22
71.49 77.71
74.14 77.85
76.79 77.04
79.44 77.04
82.09 77.48
84.73 76.33
87.38 76.9
90.03 76.24
92.68 76.78
95.33 77.17
97.97 77.04
100.62 76.8
103.27 76.92
105.92 77.15
108.57 77.7
111.21 78.12
113.86 78.52
116.51 78.28
119.16 78.85
121.81 79.01
124.45 78.68
127.1 78.83
129.75 79.26
132.4 78.31