Keshav Arora (keshav_123)

Race #1903

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Official speed 81.02 wpm (127.97 seconds elapsed during race)
Without ending ping 81.23 wpm (323 ms delay sending score to TypeRacer’s server)
Timerless 81.88 wpm (1,025 ms elapsed before first character typed; 126.62 seconds elapsed during race)
Timerless minus one 81.79 wpm, ignoring the first character typed
Race Start December 12, 2023 9:10:41am UTC
Race Finish December 12, 2023 9:12:49am UTC
Outcome No win (3 of 5)
Opponents 1. cynkhw (95.39 wpm)
Accuracy 95.9%
Points 218.75
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 understan dhowd how a change in one quantitiy y is related to a change in another. hHow does the speed of a falling object change as a function of time? Hoes dw does the level of water in a barrel change as a functiono of the amound ot of liquid oppououred inot ito it? We see change occuriring in nearly everything we objsserve in the world and unniviverse, and powerful fmovdern instriuments help us see mroe aore and more. In this section we introduce the dideadss of average and instantenaneous rates of chagnesnge, and shwo ow that they are closely related to the tslope of a fcurve at a point P on the curve. We give precise developments of these important conecepts in the next chaperter, but for now we use an informal apporaroach so you will see how they lead natuallrally to the ammain idea of this chapter, the limit. The idea of a limit placeys a foundational role throught out caclculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 1025 84 135 112 82 138 133 141 103 33 140 114 189 62 177 81 157 154 123 88 94 51 53 75 106
Character e l p s u s u n d e r s t a n d h o w -w -o -h
Milliseconds 57 119 183 125 49 74 93 89 127 282 73 164 60 119 90 96 35 148 27 67 78 76 318 127 154
Character -d - d h o w a c h a n g e i n o n e q
Milliseconds 163 114 45 103 105 59 56 97 101 100 114 77 102 76 84 112 45 53 130 81 59 124 75 77 260
Character u a n t i t i y - -y -i y i s r e l a t e d
Milliseconds 42 168 209 322 85 129 89 152 109 215 124 139 162 115 115 92 72 124 65 48 147 243 81 114 38
Character t o a c h a n g e i n a n o t h e r . h
Milliseconds 122 24 113 199 100 90 107 117 85 56 100 38 62 126 87 67 78 56 102 75 59 85 48 152 105
Character -h H o w d o e s t h e s p e e d o f a
Milliseconds 275 216 119 102 119 109 98 84 59 108 144 57 132 42 192 107 121 207 215 156 142 108 89 129 87
Character f a l l i n g o b j e c t c h a n g e a s
Milliseconds 222 265 127 149 124 101 86 178 115 205 175 36 143 179 96 165 121 111 96 65 115 86 112 79 108
Character a f u n c t i o n o f t i m e ? H o e s
Milliseconds 120 90 115 177 165 94 215 78 41 104 100 46 82 110 159 109 221 80 185 150 162 189 119 91 118
Character d -d - -s -e w d o e s t h e l e v e l o f
Milliseconds 64 232 145 136 122 42 162 134 52 136 75 92 168 88 109 88 221 45 176 113 44 134 80 67 104
Character w a t e r i n a b a r r e l c h a n g e
Milliseconds 610 88 132 154 63 71 101 139 177 65 109 138 82 94 274 120 46 150 120 63 129 87 52 137 82
Character a s a f u n c t i o n o - -o o f t h e
Milliseconds 116 67 173 60 106 74 129 175 114 222 44 33 133 123 145 337 107 139 134 64 95 165 74 94 54
Character a m o u n d o -o - -d t o f l i q u i d o -o
Milliseconds 149 89 114 68 177 142 25 168 345 133 137 39 118 99 52 103 209 108 144 107 127 184 145 322 256
Character p p o u -u -o -p o u r e d i n o t i -i - -t -o t o
Milliseconds 177 411 172 42 264 126 158 195 49 146 99 102 82 95 131 94 0 183 52 269 139 161 132 104 91
Character i t ? W e s e e c h a n g e o c c u r i
Milliseconds 120 115 52 165 177 158 216 175 118 102 167 48 152 115 56 140 25 106 41 181 397 199 43 240 102
Character -i r i n g i n n e a r l y e v e r y t h i n
Milliseconds 343 114 98 124 67 98 49 140 106 86 47 97 91 135 152 106 108 147 150 74 58 120 49 90 162
Character g w e o b j s -s -j s e r v e i n t h e w
Milliseconds 0 186 132 82 77 193 150 189 118 204 109 54 51 115 229 131 56 123 138 141 66 96 96 69 118
Character o r l d a n d u n n i v -v -i -n i v e r s e ,
Milliseconds 40 108 474 184 156 81 81 69 129 129 328 105 73 117 300 139 128 165 49 525 443 181 59 91 150
Character a n d p o w e r f u l f -f m o v -v d e r n i
Milliseconds 68 61 70 70 86 123 166 55 79 207 85 173 211 145 293 209 108 69 288 66 188 70 59 108 122
Character n s t r i -i u m e n t s h e l p u s s e e
Milliseconds 133 34 142 174 111 340 186 211 124 104 114 98 87 140 87 69 171 131 120 58 325 205 93 174 117
Character m r o e a -a - -e -o -r o r e a n d m o r e .
Milliseconds 151 113 0 93 105 61 233 146 148 140 157 238 89 49 67 118 59 103 52 118 146 123 59 49 229
Character I n t h i s s e c t i o n w e i n t r o d
Milliseconds 64 146 111 135 42 72 86 88 105 81 180 209 65 29 137 123 53 80 94 77 142 122 344 185 105
Character u c e t h e d -d i d e a d s -s -d s o f a v
Milliseconds 81 117 170 144 102 65 89 78 312 308 175 51 159 84 171 77 248 112 97 94 102 76 145 118 220
Character e r a g e a n d i n s t a n t e n -n -e a n e o
Milliseconds 174 65 94 133 122 92 85 98 70 116 125 140 61 131 91 141 200 121 169 360 122 78 153 426 110
Character u s r a t e s o f c h a g n e s -s -e -n -g n g
Milliseconds 81 65 133 158 120 179 71 80 123 46 126 43 202 112 102 131 0 154 96 270 147 147 172 179 102
Character e , a n d s h w o - -o -w o w t h a t t h
Milliseconds 50 61 157 39 132 41 137 183 69 214 29 252 230 130 128 198 93 39 151 65 110 93 107 137 71
Character e y a r e c l o s e l y r e l a t e d t o
Milliseconds 107 66 136 44 98 79 37 176 60 156 50 122 146 175 142 134 55 127 117 85 91 122 65 137 60
Character t h e t -t s l o p e o f a f -f c u r v e
Milliseconds 126 58 122 44 120 142 322 94 102 176 158 164 54 182 109 109 101 100 157 243 84 132 63 256 214
Character a t a p o i n t P o n t h e c u r v
Milliseconds 398 97 115 73 234 99 292 122 183 163 86 92 159 128 66 152 137 121 76 97 84 104 154 91 541
Character e . W e g i v e p r e c i s e d e v e l o
Milliseconds 383 123 172 247 270 133 210 58 139 145 59 107 40 83 193 130 58 92 97 132 145 198 137 51 171
Character p m e n t s o f t h e s e i m p o r t a n t
Milliseconds 100 263 68 97 133 84 121 99 123 116 154 94 118 98 99 110 61 219 179 76 110 170 109 57 163
Character c o n e -e c e p t s i n t h e n e x t c
Milliseconds 142 163 47 82 229 381 61 109 240 166 109 166 74 153 129 82 83 107 71 112 42 187 182 122 132
Character h a p e r -r -e t e r , b u t f o r n o w w
Milliseconds 131 137 291 116 56 364 281 173 142 63 79 154 187 165 68 71 170 101 120 79 137 94 52 101 126
Character e u s e a n i n f o r m a l a p p o r a -a
Milliseconds 74 108 84 84 76 124 119 92 123 84 124 66 98 99 149 59 138 131 100 108 160 141 67 115 308
Character -r -o r o a c h s o y o u w i l l s e e h
Milliseconds 120 159 88 124 67 133 120 130 211 34 100 91 69 55 92 67 94 164 144 113 71 86 169 140 217
Character o w t h e y l e a d n a t u a l l -l -l -a r a
Milliseconds 61 120 49 414 86 119 52 85 154 33 81 130 62 122 145 219 79 104 109 161 266 157 126 39 66
Character l l y t o t h e a m -m -a m a i n i d e a
Milliseconds 100 177 180 106 123 55 103 118 52 121 61 134 127 281 115 194 72 76 104 77 85 131 156 86 89
Character o f t h i s c h a p t e r , t h e l i m i
Milliseconds 103 107 74 128 45 72 96 82 136 97 78 94 168 158 78 54 137 144 84 122 0 161 256 255 174
Character t . T h e i d e a o f a l i m i t p l
Milliseconds 126 86 151 136 88 88 84 91 88 144 68 102 69 106 118 89 119 206 78 231 175 96 86 128 156
Character a c e -e -c y s a f o u n d a t i o n a l r o
Milliseconds 72 30 102 310 321 189 77 83 843 124 127 48 73 169 58 158 93 98 0 98 175 493 122 104 57
Character l e t h r o u g h t - -t o u t c a c -c l c u
Milliseconds 163 73 80 124 85 117 58 27 115 84 145 127 318 116 205 59 60 118 144 43 427 341 180 80 141
Character l u s .
Milliseconds 317 148 130 41
WPM Timing
Seconds WPM
2.56 65.64
5.12 86.74
7.68 81.27
10.24 83.22
12.8 84.4
15.36 88.3
17.92 89.08
20.47 89.67
23.03 91.17
25.59 88.15
28.15 88.23
30.71 89.87
33.27 89.08
35.83 87.08
38.39 83.15
40.95 81.76
43.51 81.91
46.07 83.09
48.63 82.92
51.19 82.75
53.75 81.27
56.31 80.35
58.87 80.73
61.42 79.32
63.98 80.46
66.54 80.97
69.1 80.23
71.66 80.54
74.22 80.35
76.78 79.86
79.34 79.71
81.9 80.73
84.46 80.28
87.02 79.98
89.58 79.71
92.14 80.23
94.7 80.72
97.26 80.57
99.82 80.31
102.37 80.76
104.93 80.85
107.49 81.27
110.05 81.45
112.61 80.99
115.17 81.58
117.73 82.05
120.29 81.9
122.85 81.76
125.41 81.43
127.97 81.02