Rajat Das (rajat_das777)

Race #1408

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Official speed 92.74 wpm (111.80 seconds elapsed during race)
Without ending ping 93.13 wpm (462 ms delay sending score to TypeRacer’s server)
Timerless 93.56 wpm (521 ms elapsed before first character typed; 110.81 seconds elapsed during race)
Timerless minus one 93.45 wpm, ignoring the first character typed
Race Start November 9, 2023 8:04:21am UTC
Race Finish November 9, 2023 8:06:13am UTC
Outcome Win (1 of 2)
Opponents 2. drarthwrarder (88.04 wpm)
Accuracy 97.3%
Points 250.40
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 unerstderstand 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 dore thes the level of water in a barerell chane as ge as af function of the amount of liquid poured into it? We see change occcururring in nearly everything we observe in the world and universe and e, and poweful rful modern in ststruments help us see more and more. In this section we introduce the idaeas of average and instanteaneous rates of change, and show theayt they are closely related to the slope of a curve a t t a ponit int P on the curve. We give precise developments of thee impse important concepts in the next chapter,, but but for anow we use oan informal approach so you will seee how they elad lead naturally to the main idea of this chapter, the limit. The idea of a limmit pit playes s 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 521 236 101 138 97 294 94 132 49 81 90 103 105 51 53 113 103 166 82 34 62 76 60 52 51
Character e l p s u s u n e r s t -t -s -r -e d e r s t a n
Milliseconds 196 63 155 149 51 83 94 85 208 176 467 90 117 78 195 156 143 133 105 117 60 72 129 111 44
Character d h o w a c h a n g e i n o n e q u a
Milliseconds 118 76 70 0 110 41 147 53 87 57 85 88 126 68 54 61 31 89 255 52 73 104 191 76 114
Character n t i t y i s r e l a t e d t o a c h a
Milliseconds 94 124 66 116 92 76 95 105 66 147 37 133 131 69 62 67 64 112 56 98 56 264 354 131 111
Character n g e i n a n o t h e r . H o w d o e s
Milliseconds 52 61 35 71 53 51 78 52 100 48 95 58 117 73 42 94 138 133 181 169 128 52 67 145 41
Character t h e s p e e d o f a f a l l i n g o b
Milliseconds 350 70 64 84 99 37 145 155 66 54 91 82 81 100 105 275 68 102 117 83 47 98 73 96 72
Character j e c t c h a n g e a s a f u n c t i o n
Milliseconds 161 45 66 133 88 97 58 101 65 81 40 76 56 82 60 91 65 106 71 147 92 230 97 52 0
Character o f t i m e ? H o w d o r e t h -h -t - -e
Milliseconds 121 73 76 81 86 52 51 78 200 92 143 164 113 90 82 48 79 0 178 84 51 239 143 145 137
Character -r e s t h e l e v e l o f w a t e r i n
Milliseconds 129 67 146 115 85 50 80 50 114 108 110 22 65 160 96 121 81 275 124 61 92 90 31 67 40
Character a b a r e -e r e l l - -l c h a n e a s
Milliseconds 74 35 158 122 262 88 54 495 99 135 0 370 261 233 137 115 134 99 93 71 108 44 117 51 33
Character - -s -a - -e g e a s a f - -f f u n c t i o n
Milliseconds 265 167 149 134 229 173 94 104 99 96 101 503 214 192 211 130 107 78 140 143 72 194 56 58 40
Character o f t h e a m o u n t o f l i q u i d
Milliseconds 75 66 105 77 86 0 80 79 170 82 53 89 172 77 68 56 88 101 94 51 119 150 44 150 93
Character p o u r e d i n t o i t ? W e s e e c h
Milliseconds 216 1677 55 84 82 116 64 211 50 38 99 93 157 66 254 68 109 149 121 116 153 148 116 132 70
Character a n g e o c c c u r -r -u -c u r r i n g i n n
Milliseconds 130 49 85 51 87 139 56 52 82 128 70 335 154 139 150 90 166 214 36 129 81 55 44 105 455
Character e a r l y e v e r y t h i n g w e o b s e r
Milliseconds 45 97 19 74 95 44 121 87 55 138 0 167 0 114 67 68 82 167 70 151 166 64 166 113 72
Character v e i n t h e w o r l d a n d u n i v e
Milliseconds 132 58 72 102 0 98 54 84 33 96 69 100 50 107 92 33 118 44 104 135 87 147 109 70 76
Character r s e a n d - -d -n -a - -e e , a n d p o w e
Milliseconds 92 104 81 161 70 80 49 90 285 133 181 175 136 151 603 138 75 53 95 72 110 71 164 0 49
Character f u l - -l -u -f r f u l m o d e r n i n s t
Milliseconds 174 91 48 130 289 120 163 133 70 257 92 85 128 188 43 172 133 34 113 112 51 97 91 233 51
Character -t -s - s t r u m e n t s h e l p u s s e e
Milliseconds 274 141 130 151 50 150 117 169 115 30 85 133 65 104 110 68 129 90 92 66 86 157 300 161 87
Character m o r e a n d m o r e . I n t h i s s e
Milliseconds 81 36 116 37 58 138 63 68 84 80 33 83 36 102 67 140 148 92 69 65 39 57 119 53 185
Character c t i o n w e i n t r o d u c e t h e i d
Milliseconds 219 197 77 40 32 127 92 97 101 61 30 73 181 49 121 109 77 57 52 137 56 39 91 81 61
Character a -a e a s o f a v e r a g e a n d i n s t
Milliseconds 220 433 52 118 112 136 115 159 110 190 129 81 101 156 69 33 68 147 50 69 94 51 39 162 48
Character a n t e -e a n e o u s r a t e s o f c h a n
Milliseconds 140 83 521 77 316 157 111 70 138 39 105 152 78 99 97 88 135 79 70 77 118 111 91 35 167
Character g e , a n d s h o w t h e -e a y -y t t h e
Milliseconds 0 135 175 118 74 57 59 114 115 32 20 133 64 143 35 68 422 166 328 401 124 112 127 106 77
Character y a r e c l o s e l y r e l a t e d t o
Milliseconds 83 86 63 50 21 135 145 119 133 47 88 69 105 40 82 51 119 119 48 44 128 54 84 64 60
Character t h e s l o p e o f a c u r v e a t
Milliseconds 65 70 32 82 97 34 166 151 45 121 63 61 135 68 105 214 83 115 241 56 39 153 96 0 216
Character - -t - t a p o n i t - -t -i -n i n t P o n
Milliseconds 268 157 161 124 126 44 172 98 151 62 0 80 124 354 137 141 152 199 35 41 188 235 116 292 38
Character t h e c u r v e . W e g i v e p r e c i
Milliseconds 88 100 82 43 103 118 47 120 184 58 104 202 387 144 151 83 137 79 32 71 45 48 54 150 96
Character s e d e v e l o p m e n t s o f t h e e i
Milliseconds 89 111 88 113 155 59 113 154 136 120 182 64 104 43 88 85 45 65 88 116 0 45 272 50 105
Character m p -p -m -i - -e s e i m p o r t a n t c o n c e
Milliseconds 63 34 332 116 149 147 221 180 66 168 45 84 55 183 67 105 158 61 66 154 120 60 84 77 56
Character p t s i n t h e n e x t c h a p t e r , ,
Milliseconds 123 50 131 0 151 34 83 45 119 0 112 123 0 230 60 140 52 119 132 58 154 79 93 59 69
Character b u t - -t -u -b - -, b u t f o r a -a n o w
Milliseconds 19 90 68 50 138 212 142 158 141 133 134 165 103 168 74 90 116 61 87 69 114 387 197 0 91
Character w e u s e o -o a n i n f o r m a l a p p
Milliseconds 139 35 98 237 113 118 96 98 68 451 150 102 117 62 34 90 115 76 89 159 39 120 59 138 100
Character r o a c h s o y o u w i l l s e e e -e h
Milliseconds 79 117 0 204 117 117 167 57 77 95 34 84 28 147 88 131 95 178 168 171 173 181 520 155 90
Character o w t h e y e l a d - -d -a -l -e l e a d n a
Milliseconds 49 110 94 120 48 93 59 89 88 0 98 72 93 220 149 140 147 131 208 42 67 84 94 108 93
Character t u r a l l y t o t h e m a i n i d e a
Milliseconds 122 134 52 98 56 96 60 70 52 82 78 40 65 64 76 83 108 96 21 122 110 119 93 84 96
Character o f t h i s c h a p t e r , t h e l i m i
Milliseconds 300 155 102 49 61 35 52 125 124 64 157 37 81 116 58 67 68 32 104 27 85 154 54 127 106
Character t . T h e i d e a o f a l i m m i t p
Milliseconds 68 177 110 42 168 47 179 71 53 140 71 102 88 77 129 58 92 280 61 122 60 25 146 80 50
Character -p - -t -i -m i t p l a y e s - -s -e s a f o u
Milliseconds 200 296 130 151 139 153 92 111 71 120 81 101 151 175 105 248 115 149 135 147 52 149 143 78 28
Character n d a t i o n a l r o l e t h r o u g h o u t
Milliseconds 156 32 187 98 81 50 35 167 41 130 57 93 126 69 68 77 101 104 46 19 123 37 155 49 100
Character c a l c u l u s .
Milliseconds 68 134 366 131 263 136 194 83 124 150
WPM Timing
Seconds WPM
2.24 80.5
4.47 93.92
6.71 85.87
8.94 96.6
11.18 98.75
13.42 104.65
15.65 105.8
17.89 109.35
20.12 109.13
22.36 106.8
24.6 105.39
26.83 98.84
29.07 94.13
31.3 95.45
33.54 94.1
35.77 93.25
38.01 93.13
40.25 92.43
42.48 94.34
44.72 96.07
46.95 92.52
49.19 90.99
51.43 89.84
53.66 90.57
55.9 92.31
58.13 93.92
60.37 93.42
62.61 93.15
64.84 94.2
67.08 93.03
69.31 94.7
71.55 95.43
73.79 93.51
76.02 93.29
78.26 93.54
80.49 93.92
82.73 92.83
84.97 94.06
87.2 92.75
89.44 92.71
91.67 92.68
93.91 93.03
96.14 92.11
98.38 92.58
100.62 93.26
102.85 94.04
105.09 93.06
107.32 92.36
109.56 93.32
111.8 92.74