rajnish (rajnishkumar31)

Race #26618

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Official speed 78.04 wpm (132.85 seconds elapsed during race)
Without ending ping 78.76 wpm (1,218 ms delay sending score to TypeRacer’s server)
Timerless 79.03 wpm (451 ms elapsed before first character typed; 131.19 seconds elapsed during race)
Timerless minus one 78.94 wpm, ignoring the first character typed
Race Start February 16, 2024 1:19:36pm UTC
Race Finish February 16, 2024 1:21:49pm UTC
Outcome Win (1 of 4)
Accuracy 95.8%
Points 210.72
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 CcaaCalculus is a t oo l that helps us understand hwo a ow a change in one quanittiy ty is related to a change in another. How does the speed of a falling object change as a function a of time? How does the level of water in a barrel chanege as a function of the amount of luiquid pouered into it? We see change occurring in heanearly everyhthing we observe in the world and univserers,e, and powerful modern instruemnments help us seem more and more. In this section we introcduce the ideas of aveaagrage adn nd instantsaaneous trates of change, and show that teythey are closely related to the slep oeppre of a curve at a point P on the curve. We give precise developments of tehsehese important concepts in teh he next chatperpter, but for noew w we use aan n informal apporoach so you will see how they lead ntaturally to the main idea of this cahapter, the limit. The idea of a limtiit plays a foundationa l role throughout calculus.
Timing
Character C c a -a -c -C a -a C a l c u l u s i s a t -
Milliseconds 451 1347 49 449 300 144 153 316 293 88 173 357 53 156 156 124 77 92 45 111 139 57 169 26 406
Character o o - l t h a t h e l p s u s u n d e r
Milliseconds 204 117 153 418 191 41 108 48 38 77 58 164 135 114 150 67 86 142 100 25 205 201 47 131 26
Character s t a n d h w o a - -a - -o -w o w a c h a
Milliseconds 216 109 88 48 115 36 183 73 21 110 50 138 287 127 214 135 207 349 94 29 274 79 197 44 95
Character n g e i n o n e q u a n i t -t -i t i y - -y
Milliseconds 81 174 74 135 113 39 72 137 74 60 83 337 67 172 345 102 153 308 112 146 80 190 83 373 115
Character t y i s r e l a t e d t o a c h a n g e
Milliseconds 83 175 54 185 81 27 229 36 101 130 56 94 208 93 245 82 64 21 165 96 114 7 197 43 73
Character i n a n o t h e r . H o w d o e s t h e
Milliseconds 95 186 28 74 146 103 132 129 116 79 48 101 74 198 115 91 104 103 81 99 44 50 110 37 47
Character s p e e d o f a f a l l i n g o b j e c
Milliseconds 20 142 57 198 160 162 64 93 105 25 46 472 199 70 101 117 100 38 35 50 232 154 126 126 167
Character t c h a n g e a s a f u n c t i o n a
Milliseconds 64 50 170 70 65 128 21 102 59 165 97 96 61 120 77 128 172 126 78 43 64 47 45 134 96
Character - -a o f t i m e ? H o w d o e s t h e l
Milliseconds 296 119 199 92 34 140 36 54 79 436 85 262 230 64 85 158 64 506 77 85 147 29 47 55 210
Character e v e l o f w a t e r i n a b a r r e l
Milliseconds 107 170 69 89 65 198 30 50 393 102 92 115 57 71 127 68 46 44 149 147 96 92 169 94 195
Character c h a n e -e g e a s a f u n c t i o n o
Milliseconds 132 146 93 7 170 120 431 132 107 129 176 50 187 0 183 117 154 161 96 80 75 72 45 104 161
Character f t h e a m o u n t o f l u -u i q u i d
Milliseconds 126 56 117 18 52 34 268 309 120 97 198 24 103 86 82 41 138 144 410 167 164 80 160 140 116
Character p o u e -e r e d i n t o i t ? W e s e e
Milliseconds 438 258 61 113 420 46 72 214 66 130 62 95 39 114 103 67 237 79 207 186 92 252 0 477 60
Character c h a n g e o c c u r r i n g i n h e a -a -e
Milliseconds 221 95 34 137 45 48 164 361 99 157 124 153 185 112 46 77 35 100 57 60 153 47 133 249 105
Character -h n e a r l y e v e r y h -h t h i n g w e o
Milliseconds 178 211 90 63 21 141 87 60 371 149 76 77 35 228 388 64 117 118 67 26 68 349 85 93 556
Character b s e r v e i n t h e w o r l d a n d u
Milliseconds 151 185 55 49 261 98 129 104 64 77 233 35 48 77 46 112 44 162 76 89 117 46 34 72 165
Character n i v s e r -r -e -s e r s , -, e , a n d p o w e
Milliseconds 199 98 132 144 57 59 317 122 115 169 17 112 243 374 33 203 30 36 83 11 95 213 235 72 43
Character r f u l m o d e r n i n s t r u e m n -n -m -e m
Milliseconds 26 251 41 143 75 211 108 610 167 13 113 83 262 56 93 149 306 94 177 11 204 263 132 218 295
Character e n t s h e l p u s s e e m - -m m o r e
Milliseconds 79 135 148 124 262 379 84 113 123 120 100 65 88 166 61 183 82 155 347 105 100 181 73 42 26
Character a n d m o r e . I n t h i s s e c t i o
Milliseconds 35 144 34 51 34 141 69 55 26 573 32 239 81 87 127 52 45 101 38 170 68 254 216 72 61
Character n w e i n t r o c -c d u c e t h e i d e a
Milliseconds 30 78 210 42 98 161 60 105 182 65 311 327 86 116 76 149 72 145 13 74 11 280 213 226 144
Character s o f a v e a a g -g -a -a r a g e a d n - -n
Milliseconds 417 51 184 72 22 413 127 135 149 108 139 269 129 195 142 99 167 69 139 68 101 0 93 416 106
Character -d n d i n s t a n t s a -a -s a n e o u s t -t r
Milliseconds 119 216 84 38 188 50 113 223 505 86 174 229 180 276 94 88 113 314 379 35 91 47 207 290 158
Character a t e s o f c h a n g e , a n d s h o w
Milliseconds 109 144 94 67 77 92 97 32 212 132 89 99 105 76 142 85 32 88 32 69 218 100 70 61 106
Character t h a t t e y -y -e -t t h e y a r e c l o s e
Milliseconds 54 73 92 74 106 76 76 137 387 128 190 443 50 51 760 83 159 87 28 59 264 75 140 50 41
Character l y r e l a t e d t o t h e s l e p - -p
Milliseconds 153 96 52 200 43 79 138 56 58 204 10 201 66 68 31 75 33 55 224 21 208 35 148 301 111
Character -e o e p -p -e p r -r e o f a c u r v e a t
Milliseconds 343 225 98 131 406 112 233 103 429 95 72 199 83 60 71 95 199 308 50 280 94 49 210 94 18
Character a p o i n t P o n t h e c u r v e . W
Milliseconds 121 63 161 349 78 34 40 132 304 225 158 66 55 120 59 17 36 211 89 65 241 122 168 52 476
Character e g i v e p r e c i s e d e v e l o p m e n
Milliseconds 239 64 166 71 125 93 79 140 143 52 256 89 87 66 66 171 140 526 140 156 274 84 154 78 146
Character t s o f t e h s e -e -s -h -e h e s e i m p o r
Milliseconds 56 47 58 106 98 101 113 81 0 204 60 287 118 234 122 235 56 198 34 51 261 52 71 68 119
Character t a n t c o n c e p t s i n t e h - -h -e h
Milliseconds 252 67 48 95 102 172 61 46 141 151 77 81 108 25 75 76 60 87 84 6 69 430 110 120 234
Character e n e x t c h a t p e r -r -e -p -t p t e r , b
Milliseconds 42 62 194 134 178 127 83 360 62 59 131 93 129 34 268 98 135 118 241 117 110 50 110 34 185
Character u t f o r n o e w - -w -e w w e u s e a
Milliseconds 87 117 56 180 68 77 71 131 78 11 37 96 346 116 117 101 86 169 18 95 276 62 43 86 109
Character a n - -n -a n i n f o r m a l a p p o -o r o a
Milliseconds 138 36 77 337 107 102 312 50 159 43 106 134 405 71 171 71 104 147 228 279 478 344 96 103 45
Character c h s o y o u w i l l s e e h o w t h
Milliseconds 476 81 47 173 79 68 141 126 46 43 151 49 183 110 104 59 79 177 133 78 78 94 70 333 41
Character e y l e a d n t -t a t u r a l l y t o t h
Milliseconds 101 113 60 144 77 94 113 87 99 201 397 106 149 121 111 44 92 107 119 66 109 49 38 66 58
Character e m a i n i d e a o f t h i s c a -a h a
Milliseconds 34 85 133 82 84 41 62 118 107 167 53 89 60 97 44 182 97 44 145 31 224 132 346 156 81
Character p t e r , t h e l i m i t . T h e i d e a
Milliseconds 127 108 95 77 61 31 125 36 56 42 411 85 127 192 96 147 41 111 102 150 161 438 87 155 54
Character o f a l i m t i -i -t i t p l a y s a f
Milliseconds 112 56 80 48 46 128 154 60 200 129 12 381 89 203 52 45 121 200 78 58 186 73 118 69 126
Character o u n d a t i o n a - l r o l e t h r o u g
Milliseconds 72 52 152 89 32 98 50 61 22 224 105 394 182 33 217 57 164 63 27 135 49 181 132 20 84
Character h o u t c a l c u l u s .
Milliseconds 106 133 73 12 64 268 150 157 299 94 519 111 132 153
WPM Timing
Seconds WPM
2.66 0
5.31 33.87
7.97 45.16
10.63 50.81
13.29 57.81
15.94 53.44
18.6 61.94
21.26 70
23.91 73.26
26.57 75.87
29.23 76.36
31.89 79.41
34.54 79.21
37.2 81.29
39.86 79.79
42.51 79.88
45.17 81.03
47.83 79.54
50.48 79.39
53.14 80.16
55.8 80.43
58.46 79.44
61.11 78.54
63.77 78.66
66.43 79.85
69.08 79.38
71.74 78.45
74.4 77.58
77.06 76.31
79.71 78.13
82.37 76.78
85.03 78.05
87.68 75.95
90.34 76.24
93 76.78
95.66 76.9
98.31 76.65
100.97 77.25
103.63 77.12
106.28 76.89
108.94 76.33
111.6 76.02
114.26 76.25
116.91 76.47
119.57 77.68
122.23 77.95
124.88 78.31
127.54 78.75
130.2 78.99
132.85 78.04