Mahdi Lotfi (mahdilotfi)

Race #9128

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Official speed 86.66 wpm (119.64 seconds elapsed during race)
Without ending ping 86.96 wpm (411 ms delay sending score to TypeRacer’s server)
Timerless 87.27 wpm (420 ms elapsed before first character typed; 118.81 seconds elapsed during race)
Timerless minus one 87.17 wpm, ignoring the first character typed
Race Start December 31, 2024 7:16:58pm UTC
Race Finish December 31, 2024 7:18:57pm UTC
Outcome No win (2 of 4)
Opponents 1. breakingpoint1 (96.39 wpm)
Accuracy 97.8%
Points 233.98
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 Calculauus 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? hoHow does the evelevel of water in a barrel change as a function of the amount of liquid proured into it? We see change occurring in rnnearly everything we observe in the world and univers, ee, and powerful modern insturruments help us wsee more and more. In this section we introduce the ideas of average oaand instantaneous rates of change, and hshow theat they are closeelly related to the slope of a couurve at a point P on the cursvve. We give precise developments of these iportmporatant concepts in the next chapter, but for now we use an informarl l al approach so you will see how they lead naturally to the main idea of this chapter, the limit. The idea of a litmmit plays a foundational role throughout claalculus.
Timing
Character C a l c u l a u -u -a u s i s a t o o l t h
Milliseconds 420 171 90 118 117 148 83 200 229 141 196 115 76 116 138 34 168 87 181 39 130 174 35 133 56
Character a t h e l p s u s u n d e r s t a n d h o
Milliseconds 80 53 45 172 97 56 172 90 116 116 81 85 209 176 21 204 67 244 69 98 194 153 74 156 63
Character w a c h a n g e i n o n e q u a n t i t
Milliseconds 42 61 138 67 150 97 99 65 154 115 93 123 73 86 233 84 97 97 169 53 158 64 225 98 328
Character y i s r e l a t e d t o a c h a n g e
Milliseconds 132 71 211 123 84 207 70 141 129 96 67 189 87 146 41 51 88 117 132 79 111 46 130 77 71
Character i n a n o t h e r . H o w d o e s t h e
Milliseconds 81 79 72 182 95 98 62 147 78 90 51 82 236 154 46 127 143 92 60 130 101 244 103 67 98
Character s p e e d o f a f a l l i n g o b j e c t
Milliseconds 82 110 80 136 203 76 97 103 61 117 59 123 150 68 135 148 33 116 69 167 102 89 169 144 181
Character c h a n g e a s a f u n c t i o n o f
Milliseconds 56 176 94 77 81 99 117 67 98 150 98 135 58 124 66 165 66 176 41 88 71 87 96 132 32
Character t i m e ? h o -o -h H o w d o e s t h e e v
Milliseconds 228 79 64 84 245 121 194 201 261 126 276 165 117 50 139 71 92 137 118 159 70 103 119 320 256
Character e -e -v -e l e v e l o f w a t e r i n a b
Milliseconds 114 172 146 124 259 113 159 78 85 41 173 60 60 180 170 70 203 80 66 86 61 70 115 83 133
Character a r r e l c h a n g e a s a f u n c t i o
Milliseconds 91 254 179 75 134 122 222 66 90 51 132 38 145 51 151 114 117 99 90 127 158 91 177 66 73
Character n o f t h e a m o u n t o f l i q u i d
Milliseconds 77 118 73 119 15 155 77 70 117 70 143 201 98 159 115 116 101 150 12 139 115 294 88 66 324
Character p r -r o u r e d i n t o i t ? W e s e e
Milliseconds 79 208 139 295 231 70 77 206 226 114 85 74 151 30 71 136 115 245 91 420 184 94 133 175 151
Character c h a n g e o c c u r r i n g i n r n -n -r
Milliseconds 150 205 90 91 79 160 33 113 253 126 119 117 117 348 117 75 114 80 96 59 90 245 139 222 121
Character n e a r l y e v e r y t h i n g w e o b s e
Milliseconds 185 96 101 50 117 213 85 164 155 215 51 65 133 98 24 134 117 65 118 87 121 113 127 276 210
Character r v e i n t h e w o r l d a n d u n i v
Milliseconds 46 223 109 72 100 96 88 210 81 70 67 126 55 128 37 145 6 190 97 117 39 150 167 74 85
Character e r s , e -e - -, e , a n d p o w e r f u l
Milliseconds 233 116 137 89 44 15 389 131 123 167 88 25 80 130 43 120 133 54 81 73 50 238 59 160 102
Character m o d e r n i n s t u r -r -u r u m e n t s h e
Milliseconds 222 176 192 211 73 146 101 80 88 207 156 116 46 339 131 153 69 188 107 65 115 136 65 180 132
Character l p u s w -w s e e m o r e a n d m o r e
Milliseconds 58 167 74 133 95 66 219 288 124 170 164 87 181 95 73 61 54 158 66 103 81 60 83 116 47
Character . I n t h i s s e c t i o n w e i n t r
Milliseconds 99 140 406 309 85 210 54 64 51 62 166 183 170 183 94 92 107 115 90 100 118 169 44 118 138
Character o d u c e t h e i d e a s o f a v e r a g
Milliseconds 58 200 94 125 223 56 190 65 84 70 78 95 161 102 226 162 83 157 61 280 157 187 232 73 146
Character e o a -a -o a n d i n s t a n t a n e o u s r
Milliseconds 65 93 119 146 130 142 248 104 83 89 94 82 117 136 63 131 559 105 126 389 184 70 116 57 517
Character a t e s o f c h a n g e , a n d h -h s h o
Milliseconds 85 176 65 216 72 118 146 74 339 80 79 81 85 88 154 58 120 77 72 77 220 263 147 58 69
Character w t h e -e a t t h e y a r e c l o s e e l
Milliseconds 60 69 125 64 85 322 115 48 83 148 102 82 78 76 89 77 74 116 127 75 140 97 124 296 78
Character -l -e l y r e l a t e d t o t h e s l o p e
Milliseconds 273 120 281 114 115 289 59 191 125 127 67 211 118 178 80 22 116 100 63 105 86 131 195 215 157
Character o f a c o u -u -o u r v e a t a p o i n
Milliseconds 80 85 121 64 164 103 237 75 118 274 193 204 80 298 160 112 193 21 82 144 67 137 35 185 114
Character t P o n t h e c u r s v -v -s v e . W e
Milliseconds 81 116 228 211 174 54 79 99 120 50 115 138 107 125 207 162 295 139 43 168 79 104 239 167 84
Character g i v e p r e c i s e d e v e l o p m e n t s
Milliseconds 163 80 148 65 101 173 124 50 221 77 303 161 96 113 166 187 84 196 156 99 226 115 113 87 179
Character o f t h e s e i p o r t -t -r -o -p m p o r a -a
Milliseconds 89 126 158 35 294 71 116 152 138 98 94 211 52 111 137 238 206 65 127 221 172 55 139 284 273
Character t a n t c o n c e p t s i n t h e n e x t
Milliseconds 139 145 94 92 147 185 82 64 105 193 92 101 275 92 100 86 82 96 121 62 118 45 111 189 173
Character c h a p t e r , b u t f o r n o w w e
Milliseconds 117 117 78 148 161 166 217 83 65 29 180 94 99 85 188 80 78 78 130 106 211 188 347 86 170
Character u s e a n i n f o r m a r l - -l -r -a l - -l
Milliseconds 141 118 166 101 169 134 80 122 85 76 126 39 126 152 84 71 190 332 130 128 132 206 102 259 118
Character a l a p p r o a c h s o y o u w i l l s
Milliseconds 170 98 83 133 66 115 91 74 105 185 80 86 191 121 47 235 101 57 80 101 116 99 132 40 101
Character e e h o w t h e y l e a d n a t u r a l l
Milliseconds 177 122 103 167 54 70 81 108 96 78 93 58 121 86 114 176 93 158 117 162 85 108 51 66 120
Character y t o t h e m a i n i d e a o f t h i
Milliseconds 160 83 139 107 91 228 59 122 40 304 207 83 67 87 103 130 167 96 39 75 110 180 292 103 52
Character s c h a p t e r , t h e l i m i t . T h e
Milliseconds 69 75 163 122 186 460 280 207 56 64 39 205 23 137 44 121 66 181 75 248 121 112 234 118 119
Character i d e a o f a l i t m -m -t m i t p l a y
Milliseconds 58 344 148 154 112 41 87 103 68 148 54 141 87 131 68 360 131 265 76 194 91 292 135 118 83
Character s a f o u n d a t i o n a l r o l e t h r
Milliseconds 115 109 72 88 173 79 55 163 53 177 63 52 85 70 221 107 100 236 49 166 96 58 124 72 85
Character o u g h o u t c l a -a -l a l c u l u s .
Milliseconds 47 81 68 102 281 64 98 86 229 93 74 427 143 79 116 130 94 278 91 214 89
WPM Timing
Seconds WPM
2.39 60.18
4.79 85.26
7.18 91.94
9.57 91.52
11.96 96.29
14.36 97.79
16.75 100.3
19.14 100.93
21.54 98.63
23.93 95.29
26.32 94.83
28.71 95.29
31.11 96.44
33.5 94.21
35.89 93.61
38.28 93.09
40.68 92.04
43.07 92.22
45.46 93.7
47.86 92.78
50.25 91.94
52.64 91.41
55.03 91.58
57.43 91.52
59.82 91.88
62.21 90.66
64.61 90.09
67 89.91
69.39 89.75
71.78 89.27
74.18 89.46
76.57 88.55
78.96 88.75
81.36 88.21
83.75 88.12
86.14 88.18
88.53 86.48
90.93 86.84
93.32 87.18
95.71 87.14
98.1 85.75
100.5 86.09
102.89 86.77
105.28 87.08
107.68 87.04
110.07 87.11
112.46 86.86
114.85 87.03
117.25 87.51
119.64 86.66