py (pytech)

Race #11584

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Official speed 91.89 wpm (112.83 seconds elapsed during race)
Without ending ping 92.27 wpm (336 ms delay sending score to TypeRacer’s server)
Timerless 92.70 wpm (522 ms elapsed before first character typed; 111.97 seconds elapsed during race)
Timerless minus one 92.59 wpm, ignoring the first character typed
Race Start August 29, 2023 9:36:37am UTC
Race Finish August 29, 2023 9:38:30am UTC
Outcome Win (1 of 4)
Accuracy 97.7%
Points 248.11
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 quanitttity is related to a change in another. How does the speed of a falling object hcchange 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 ee change aoccurring in nearly everything we obseverrve in the world and universe, and powerful modern instruments help us see more and more. In this section we introduce itthe ideas of average and instantaneous rates of change, and hoshow that they are closlelely related to the slope of a curve at a point P on the curve. We giveive pricecide se developments of these important concepts in the next chapter, but for now we sueuse an informal appraooach so you will sooee how they lead naturally to the main idea of this chapter, the limit. The ideaidea of a limit plays a foundational role througout hout acalculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 522 328 11 111 219 261 84 263 35 264 74 24 181 67 45 188 76 46 156 42 81 201 3 46 74
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 192 5 83 285 38 105 200 32 107 39 113 200 91 70 5 141 5 60 157 92 153 0 163 445 113
Character c h a n g e i n o n e q u a n i t t -t -t -i t
Milliseconds 63 69 198 0 71 192 68 192 0 120 231 0 178 75 261 46 329 0 235 0 129 298 191 186 223
Character i t y i s - r e l a t e d t o a c h a
Milliseconds 197 16 90 181 297 69 2 0 428 270 32 28 262 0 175 0 117 81 176 60 128 113 55 62 229
Character n g e i n a n o t h e r . H o w d o e s
Milliseconds 0 51 187 63 169 0 84 161 0 121 0 86 142 37 124 93 239 225 3 114 56 208 112 47 31
Character t h e s p e e d o f a f a l l i n g o b
Milliseconds 44 78 136 32 142 72 130 72 30 150 158 0 105 166 119 33 190 287 166 265 3 0 53 258 0
Character j e c t h c -c -h c h a n g e a s a f u n c
Milliseconds 135 213 0 24 163 254 43 235 190 76 94 192 0 82 199 52 235 64 36 143 67 47 113 48 77
Character t i o n o f t i m e ? H o w d o e s t h
Milliseconds 53 163 201 0 83 206 0 125 63 220 0 165 282 230 218 273 2 94 73 162 106 26 45 52 46
Character e l e v e l o f w a t e r i n a b a r
Milliseconds 221 130 99 153 20 224 0 104 168 15 378 68 205 0 173 45 82 123 0 71 110 143 196 165 181
Character r e l c h a n g e a s a f u n c t i o n
Milliseconds 80 247 4 93 181 96 178 0 58 189 61 197 67 51 200 127 46 136 39 81 63 181 245 0 127
Character o f t h e a m o u n t o f l i q u i d p
Milliseconds 217 2 110 47 67 130 54 188 0 287 3 0 2 180 244 2 142 121 166 39 89 268 28 145 164
Character o u r e d i n t o i t ? W e s e e - -e
Milliseconds 188 0 113 175 3 105 161 0 0 282 44 238 0 471 206 244 117 169 0 184 71 81 101 854 0
Character -e - e e c h a n g e a -a o c c u r r i n g i
Milliseconds 0 0 46 83 163 105 30 201 4 74 172 44 137 174 234 0 145 407 182 77 296 0 0 62 234
Character n n e a r l y e v e r y t h i n g w e o b
Milliseconds 0 84 78 222 114 23 27 71 192 286 0 184 32 18 51 106 155 16 21 140 55 184 71 226 0
Character s e v e r -r -e -v r v e i n t h e w o r l d
Milliseconds 366 130 0 279 4 177 186 188 202 39 227 47 229 0 79 24 90 151 34 34 206 151 3 41 144
Character a n d u n i v e r s e , a n d p o w e r f u
Milliseconds 161 0 45 148 183 58 255 2 221 84 39 115 96 76 201 0 70 126 116 151 31 195 55 90 68
Character l m o d e r n i n s t r u m e n t s h e l p
Milliseconds 73 154 132 166 4 192 43 2 179 247 5 135 0 78 0 80 250 0 41 161 53 130 142 37 66
Character u s s e e m o r e a n d m o r e . I n
Milliseconds 86 152 334 68 213 56 84 144 45 135 63 117 47 117 38 52 145 65 143 85 76 153 92 264 138
Character t h i s s e c t i o n w e i n t r o d u c
Milliseconds 195 98 80 132 79 33 187 70 43 48 118 205 0 96 139 154 97 166 1 7 178 138 54 110 105
Character e i t -t -i t h e i d e a s o f a v e r a g
Milliseconds 194 77 215 0 269 190 78 109 121 41 179 33 181 127 102 58 126 0 109 211 46 287 83 136 21
Character e a n d i n s t a n t a n e o u s r a t e s
Milliseconds 167 78 148 10 86 132 183 0 115 0 103 18 166 421 140 294 231 0 139 57 269 122 13 200 109
Character o f c h a n g e , a n d h o -o -h s h o w
Milliseconds 51 166 0 114 117 59 207 0 86 209 90 77 176 22 36 142 115 138 234 189 176 19 140 0 95
Character t h a t t h e y a r e c l o s l e l -l -e -l e
Milliseconds 80 89 298 0 88 99 140 219 0 176 178 91 43 105 93 107 140 224 0 121 159 155 193 191 279
Character l y r e l a t e d t o t h e s l o p e o
Milliseconds 86 94 166 199 81 0 210 0 185 0 105 96 164 47 52 80 140 40 171 4 127 187 207 94 166
Character f a c u r v e a t a p o i n t P o n
Milliseconds 3 98 158 86 38 95 209 87 221 47 220 3 124 265 83 78 173 153 4 2 108 369 206 212 0
Character t h e c u r v e . W e g i v e - -i -v -e i
Milliseconds 108 30 60 150 41 246 54 221 78 190 175 80 238 144 76 0 152 196 9 185 360 0 0 0 155
Character v e p r i c -c -i e c i d e - -e -d s e d e v e
Milliseconds 40 161 70 159 153 72 73 302 180 170 0 208 23 182 159 169 190 200 186 87 93 82 127 81 158
Character l o p m e n t s o f t h e s e i m p o r t a
Milliseconds 49 242 4 0 259 0 0 155 39 235 0 87 42 52 114 94 114 207 115 0 31 234 54 4 176
Character n t c o n c e p t s i n t h e n e x t c
Milliseconds 0 58 157 105 148 0 66 207 5 184 184 71 167 0 86 7 90 132 60 53 171 0 0 133 200
Character h a p t e r , b u t f o r n o w w e s u
Milliseconds 86 324 2 172 238 62 173 43 75 84 113 497 81 177 79 37 58 154 3 80 81 170 92 140 0
Character e -e -u -s u s e a n i n f o r m a l a p p r a
Milliseconds 269 113 218 204 75 189 95 54 148 2 150 196 2 4 307 35 38 208 128 239 165 28 173 174 113
Character o -o -a o a c h s o y o u w i l l s o o -o -o
Milliseconds 28 363 195 285 140 15 87 164 177 78 93 166 280 0 88 9 235 0 91 145 132 34 77 385 183
Character e e h o w t h e y l e a d n a t u r a l l
Milliseconds 182 70 189 51 133 4 77 62 56 187 2 81 92 215 43 5 92 62 224 0 42 141 381 71 142
Character y t o t h e m a i n i d e a o f t h i
Milliseconds 58 146 127 192 33 31 73 161 45 61 203 100 0 71 185 0 211 47 141 120 0 125 55 25 180
Character s c h a p t e r , t h e l i m i t . T h e
Milliseconds 269 135 229 72 272 0 121 223 58 202 76 279 321 147 113 274 151 68 167 2 207 81 252 43 149
Character i -i d e a $i -e -a d e a o f a l i m i t p
Milliseconds 74 176 9 14 173 98 680 0 0 19 200 67 85 134 0 104 146 95 175 166 61 184 0 108 122
Character l a y s a f o u n d a t i o n a l r o l e
Milliseconds 32 237 4 169 48 175 96 40 210 3 0 41 190 36 131 210 4 251 52 220 233 58 83 213 55
Character t h r o u g o u t - -t -u -o h o u t a -a c a l c
Milliseconds 92 75 188 92 2 5 459 5 10 184 379 196 180 328 206 409 5 9 157 323 364 162 165 0 231
Character u l u s .
Milliseconds 108 148 108 248 134
WPM Timing
Seconds WPM
2.26 63.81
4.51 93.06
6.77 97.49
9.03 90.4
11.28 84.02
13.54 89.51
15.8 94.96
18.05 95.05
20.31 94.54
22.57 94.66
24.82 95.72
27.08 96.16
29.34 97.35
31.59 98.38
33.85 98.2
36.11 94.72
38.36 94.15
40.62 95.72
42.88 93.48
45.13 94.66
47.39 96.23
49.65 96.93
51.9 97.57
54.16 98.38
56.42 97.63
58.67 98.38
60.93 97.69
63.19 97.43
65.44 97.55
67.7 96.43
69.95 96.92
72.21 96.55
74.47 96.52
76.72 94.94
78.98 94.05
81.24 95.13
83.49 95.72
85.75 95.86
88.01 95.17
90.26 94.12
92.52 94.16
94.78 94.45
97.03 94.85
99.29 94.75
101.55 94.3
103.8 93.75
106.06 94.36
108.32 94.28
110.57 92.9
112.83 91.89