jai (predator726)

Race #17497

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Official speed 85.51 wpm (121.25 seconds elapsed during race)
Without ending ping 85.77 wpm (363 ms delay sending score to TypeRacer’s server)
Timerless 86.50 wpm (1,024 ms elapsed before first character typed; 119.86 seconds elapsed during race)
Timerless minus one 86.40 wpm, ignoring the first character typed
Race Start February 16, 2025 11:34:37am UTC
Race Finish February 16, 2025 11:36:39am UTC
Outcome Win (1 of 5)
Opponents 3. ahnfnsr (80.40 wpm)
5. turbo_ultimatum (76.87 wpm)
Accuracy 96.6%
Points 230.88
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 help suss us understand how a cahnghang eine 9nin one quantity is related to a change in another. How does the speed of a falling object change as as function of time? How does the level of water in a braarerel change as a function of the amount of alluqiiquid poured ointo it? We see change occurinring in nearly everything we observe in the worold and universe, a nd poewrfwerful modern instrumetns hnts help us seej more and more. In this section we introduce the idea ss of average and instantaneiousous rates of change, and show that they are closely related to the slop ee of a curve at a point P on the curve. We give precise develomentpments of these important concepts in the next chapter bu, but for now we use ian infomralrmal approach s yo you will see how they lead fnntuaturally to the main idea of this chapter, the limit. The idea of a limit plays a foundational role through out calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 1024 119 120 190 257 145 240 108 51 138 85 51 140 88 147 66 92 182 129 137 49 81 34 43 143
Character e l p s u s -s -u -s - s u s u n d e r s t a n
Milliseconds 72 75 151 146 0 152 96 185 121 126 155 112 56 93 182 91 146 162 40 161 54 104 98 271 96
Character d h o w a c a h n g -g -n -h -a h a n g e i n
Milliseconds 27 116 124 83 49 70 113 87 395 138 18 161 28 354 100 138 130 186 81 103 132 98 15 123 129
Character -n -i -e - e 9 n -n -9 i n o n e q u a n t i t y
Milliseconds 229 135 119 118 116 107 84 142 281 120 345 135 95 106 97 84 47 219 101 103 85 131 107 101 155
Character i s r e l a t e d t o a c h a n g e i
Milliseconds 77 118 83 42 166 75 110 146 78 71 151 82 134 117 119 185 114 265 81 65 85 48 65 52 105
Character n a n o t h e r . H o w d o e s t h e s
Milliseconds 110 91 77 102 84 68 65 29 100 55 84 164 80 52 64 108 84 90 54 52 133 37 76 50 120
Character p e e d o f a f a l l i n g o b j e c t
Milliseconds 113 50 139 162 22 77 413 176 123 86 169 117 69 180 250 117 106 61 129 94 92 73 180 144 65
Character c h a n g e a s a s - -s f u n c t i o n
Milliseconds 171 63 61 96 31 80 68 64 124 57 124 482 82 267 120 187 146 148 161 44 171 54 119 102 142
Character o f t i m e ? H o w d o e s t h e l e v
Milliseconds 111 77 87 162 42 99 77 167 102 160 87 72 65 169 99 256 73 99 103 66 117 61 138 82 147
Character e l o f w a t e r i n a b r a -a -r a r e
Milliseconds 86 55 61 87 48 66 102 85 78 89 94 35 98 114 84 115 71 117 227 189 279 104 117 69 98
Character -e r e l c h a n g e a s a f u n c t i o n
Milliseconds 467 197 102 162 140 214 62 72 81 20 66 84 76 105 47 100 98 170 316 154 66 166 33 113 106
Character o f t h e a m o u n t o f a l -l -a l u q
Milliseconds 85 62 81 36 152 34 47 51 263 103 134 112 196 105 94 157 50 50 163 0 345 103 237 162 138
Character i -i -q -u i q u i d p o u r e d o -o i n t o i
Milliseconds 66 287 92 170 385 214 86 215 115 87 159 171 136 95 103 148 50 116 280 190 129 50 88 66 216
Character t ? W e s e e c h a n g e o c c u r i n -n
Milliseconds 145 289 102 123 101 126 199 89 143 84 148 66 61 73 51 69 74 190 143 117 139 116 99 113 279
Character -i r i n g i n n e a r l y e v e r y t h i n
Milliseconds 109 165 165 105 94 51 101 83 120 133 62 70 47 81 152 72 80 143 106 67 119 101 112 103 110
Character g w e o b s e r v e i n t h e w o r o -o
Milliseconds 55 87 101 79 97 156 97 169 100 94 213 109 109 165 126 100 29 133 31 56 117 64 82 189 378
Character l d a n d u n i v e r s e , a - n d p o
Milliseconds 203 80 68 119 49 77 41 167 172 125 64 138 113 100 83 83 92 101 77 306 228 146 30 139 134
Character e w r f -f -r -w -e w e r f u l m o d e r n i n s
Milliseconds 93 0 78 161 261 103 147 128 151 26 125 340 134 134 91 160 110 131 137 55 66 107 91 126 83
Character t r u m e t n s h -h - -s -n -t n t s h e l p u
Milliseconds 105 133 97 150 69 103 15 112 67 156 160 116 150 146 157 202 182 149 112 142 64 100 165 117 238
Character s s e e j - -j m o r e a n d m o r e .
Milliseconds 106 76 159 138 137 129 35 596 195 186 188 80 68 64 38 163 48 106 48 183 133 99 36 85 95
Character I n t h i s s e c t i o n w e i n t r o d
Milliseconds 221 130 100 68 80 67 22 83 215 68 200 165 28 104 133 99 46 106 92 140 115 66 150 86 120
Character u c e t h e i d e a s -s - s o f a v e r
Milliseconds 138 88 164 50 122 60 52 71 114 54 200 94 107 159 207 130 113 80 74 21 101 194 136 158 72
Character a g e a n d i n s t a n t a n e i o u s -s -u -o
Milliseconds 132 113 72 51 100 68 59 67 118 105 97 101 118 32 114 537 141 211 146 93 104 104 182 120 140
Character -i o u s r a t e s o f c h a n g e , a n d
Milliseconds 122 218 94 125 30 214 120 67 82 201 149 166 213 105 211 67 56 92 50 53 64 98 75 65 28
Character s h o w t h a t t h e y a r e c l o s e
Milliseconds 75 162 85 115 36 78 49 73 51 49 51 151 0 130 33 65 116 377 91 165 202 120 147 61 54
Character l y r e l a t e d t o t h e s l o p e -e
Milliseconds 100 150 82 129 69 258 139 57 77 151 65 88 55 73 102 51 39 85 61 68 264 148 122 19 340
Character - e o f a c u r v e a t a p o i n t
Milliseconds 122 232 119 109 27 92 104 104 131 176 91 228 55 65 208 94 75 137 119 248 215 121 119 80 75
Character P o n t h e c u r v e . W e g i v e p
Milliseconds 826 148 128 105 100 99 54 41 56 162 102 81 191 91 117 91 131 99 85 114 96 74 51 63 164
Character r e c i s e d e v e l o m e n t -t -n -e -m p m e n
Milliseconds 164 110 180 79 203 82 102 160 165 116 87 78 158 281 77 108 32 204 116 134 434 271 185 73 136
Character t s o f t h e s e i m p o r t a n t c o n
Milliseconds 24 107 61 156 80 55 115 66 19 161 86 63 106 151 130 134 51 183 115 37 99 100 150 67 95
Character c e p t s i n t h e n e x t c h a p t e r
Milliseconds 84 151 116 101 176 52 118 103 102 90 102 521 151 133 66 193 153 82 121 54 80 199 131 103 99
Character b u -u -b - , b u t f o r n o w w e u s
Milliseconds 229 81 108 212 121 309 187 119 54 142 71 84 115 68 132 180 182 98 43 83 211 86 96 138 76
Character e i -i a n i n f o m r a l -l -a -r -m r m a l a
Milliseconds 51 85 147 305 84 101 97 102 126 110 85 91 40 166 115 195 119 152 112 220 118 117 67 133 147
Character p p r o a c h s y -y - o y o u w i l l s
Milliseconds 283 134 98 105 168 178 82 81 125 132 82 316 118 198 114 102 91 80 56 66 91 136 131 112 86
Character e e h o w t h e y l e a d f n -n -f n t u -u
Milliseconds 68 133 77 132 67 70 81 198 23 67 81 71 164 70 99 117 144 501 136 210 105 202 161 125 233
Character -t a t u r a l l y t o t h e m a i n i d e
Milliseconds 126 168 95 136 67 120 117 224 223 68 115 67 84 166 62 50 59 167 145 100 135 116 260 323 175
Character a o f t h i s c h a p t e r , t h e l i
Milliseconds 92 180 150 100 53 133 36 160 82 71 146 82 49 182 135 100 98 58 79 116 54 43 106 135 65
Character m i t . T h e i d e a o f a l i m i t
Milliseconds 199 136 81 88 113 219 94 23 101 167 117 165 88 125 98 84 37 160 119 137 132 152 132 121 56
Character p l a y s a f o u n d a t i o n a l r o l e
Milliseconds 156 148 52 131 185 148 118 92 125 132 68 161 38 129 91 60 116 119 300 136 133 165 78 154 78
Character t h r o u g h - o u t c a l c u l u s .
Milliseconds 65 207 52 147 95 25 144 54 109 398 189 87 77 67 172 136 115 181 196 197 301 134 103
WPM Timing
Seconds WPM
2.42 49.48
4.85 69.28
7.27 79.18
9.7 68.04
12.12 62.35
14.55 70.1
16.97 78.47
19.4 82.27
21.82 85.77
24.25 83.13
26.67 85.47
29.1 87.01
31.52 86.79
33.95 88.01
36.37 84.45
38.8 83.2
41.22 84.42
43.65 84.12
46.07 85.95
48.5 86.1
50.92 86.25
53.35 84.8
55.77 83.69
58.2 83.3
60.62 83.33
63.05 84.51
65.47 84.86
67.9 85.36
70.32 84.12
72.75 85.94
75.17 86.04
77.6 86.13
80.02 86.37
82.45 86.31
84.87 86.81
87.3 85.5
89.72 86.53
92.15 86.47
94.57 85.77
97 85.98
99.42 85.09
101.85 84.95
104.27 85.51
106.7 84.35
109.12 84.45
111.55 85.2
113.97 85.6
116.4 85.98
118.82 85.94
121.25 85.51