mrkit (itrolode)

Race #616

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Official speed 74.65 wpm (138.89 seconds elapsed during race)
Without ending ping 74.76 wpm (202 ms delay sending score to TypeRacer’s server)
Timerless 74.94 wpm (336 ms elapsed before first character typed; 138.35 seconds elapsed during race)
Timerless minus one 74.85 wpm, ignoring the first character typed
Race Start February 11, 2025 12:06:50pm UTC
Race Finish February 11, 2025 12:09:09pm UTC
Outcome Win (1 of 3)
Accuracy 95.8%
Points 201.55
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 understand how a change in one quantity is realtlated to chaa change in another. How does the speed of afa faillling object change as a function of time? HOwow does the level of water in a barrel changes as a function f of the amount of liquid poured into it? We see change ofcccurring in nreaeaearly everything we observe in the world and universe, and powerful modern isnstrument sss help use sees more and more. In this section we introduece the idea os of avearrage and instantaneioous rate s of change, and show that they are closely reallated to atthe sloppee fo of a curve at a Ppoin t P on the cruvurve. JWWe give precise develppopments of these important conecepts int the next hchapter, but for now we use an infromormal approcach so you will see how they lead naturally to the main idea of this chapter, the limint. The liidea of a limit play as a foundational reolole throughtoutout calculaus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 336 444 152 122 287 146 295 113 52 173 134 71 155 111 114 75 124 136 136 280 94 45 91 66 258
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 83 124 142 104 23 122 93 95 142 145 83 146 91 114 162 191 345 112 124 174 89 117 67 136 111
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 126 77 70 95 103 154 128 98 120 107 117 123 51 126 160 93 134 140 156 91 109 143 131 111 95
Character r e a l t -t -l -a l a t e d t o c h a -a -h -c a
Milliseconds 100 113 75 58 77 148 168 104 118 185 9 171 94 85 65 185 38 180 164 126 103 165 116 118 110
Character c h a n g e i n a n o t h e r . H o w d
Milliseconds 91 145 74 129 54 233 118 108 55 108 139 168 64 53 89 129 82 107 88 114 196 97 91 138 104
Character o e s t h e s p e e d o f a f a -a -f f a
Milliseconds 102 98 34 74 232 175 157 91 124 103 146 183 183 84 67 95 113 107 416 70 236 106 328 128 84
Character i l -l -i l l i n g o b j e c t c h a n g e a
Milliseconds 32 140 430 118 196 116 102 128 70 62 74 146 201 108 171 147 134 253 63 109 95 115 147 145 207
Character s a f u n c t i o n o f t i m e ? H O w
Milliseconds 129 146 104 135 387 80 158 423 173 60 122 93 99 104 108 124 104 53 130 55 242 136 168 57 143
Character -w -O o w d o e s t h e l e v e l o f w a
Milliseconds 298 129 141 64 128 126 94 94 66 92 102 98 56 83 105 78 147 161 46 102 130 23 207 135 81
Character t e r i n a b a r r e l c h a n g e s -s
Milliseconds 118 126 84 57 71 102 132 134 112 149 91 106 214 226 102 127 132 76 67 100 97 145 90 370 152
Character a s a f u n c t i o n f - -f o f t h e
Milliseconds 120 108 84 123 96 117 71 148 89 129 13 93 107 115 173 122 407 325 181 75 68 130 80 84 65
Character a m o u n t o f l i q u i d p o u r e d i
Milliseconds 168 145 137 113 146 78 84 96 142 134 188 130 157 77 94 97 92 237 138 170 112 103 78 73 84
Character n t o i t ? W e s e e c h a n g e o f c
Milliseconds 110 85 71 123 172 85 346 98 283 233 129 142 92 152 60 165 37 100 98 95 134 118 89 127 265
Character -c -f c c u r r i n g i n n r e a -a -e e a -a -e -r
Milliseconds 156 117 128 140 86 384 165 109 106 70 54 80 114 94 232 104 64 122 246 118 151 72 266 113 124
Character e a r l y e v e r y t h i n g w e o b s e r
Milliseconds 74 60 119 69 166 97 124 165 154 70 366 124 107 82 130 36 99 112 88 114 166 152 384 100 147
Character v e i n t h e w o r l d a n d u n i v e
Milliseconds 251 147 71 50 127 122 94 85 72 69 104 82 87 94 122 64 122 73 78 76 124 156 110 93 141
Character r s e , a n d p o w e r f u l m o d e r n
Milliseconds 79 136 112 131 100 95 74 72 54 82 128 154 97 84 188 62 154 128 253 107 95 167 94 130 115
Character i s -s n s t r u m e n t s -s s -s - s h e l p
Milliseconds 106 371 262 133 92 103 130 103 190 81 96 51 205 186 105 173 258 128 114 94 129 96 77 168 270
Character u s e - -e s e e s - -s m o r e a n d m
Milliseconds 125 137 131 180 159 114 124 127 66 162 8 181 203 109 163 157 107 57 69 74 122 53 113 61 92
Character o r e . I n t h i s s e c t i o n w e i
Milliseconds 108 46 64 132 85 173 104 102 98 64 95 24 105 90 69 192 158 39 62 140 110 158 99 142 183
Character n t r o d u e -e c e t h e i d e a o -o - s
Milliseconds 132 181 130 75 239 86 101 383 101 143 54 121 51 83 71 46 113 399 105 120 64 336 106 197 93
Character o f a v e a r -r -a r a g e a n d i n s t a n
Milliseconds 100 134 170 173 354 192 155 133 260 106 153 96 136 148 88 150 90 135 31 86 118 72 99 89 436
Character t a n e i o -o -i o u s r a t e - s o f c h
Milliseconds 1011 115 142 418 218 46 304 96 175 105 146 92 142 90 145 100 85 289 312 95 82 124 76 346 74
Character a n g e , a n d s h o w t h a t t h e y
Milliseconds 72 124 214 132 96 76 107 91 66 101 392 80 84 86 119 151 91 53 79 84 128 70 94 67 92
Character a r e c l o s e l y r e a l -l -a l a t e d t
Milliseconds 77 110 83 99 242 42 134 116 96 356 156 112 105 75 100 90 318 87 179 47 109 120 69 133 136
Character o a t -t -a t h e s l o p p e -e -p e f o - -o
Milliseconds 82 114 7 118 213 112 220 112 62 83 167 90 158 176 556 321 178 151 124 105 119 50 128 336 112
Character -f o f a c u r v e a t a P -P p o i n -
Milliseconds 124 326 110 86 134 130 748 127 121 206 134 108 113 202 145 140 122 384 355 229 126 124 105 114 357
Character t P o n t h e c r u v -v -u -r u r v e . J
Milliseconds 302 123 215 135 127 130 148 107 101 53 93 160 146 95 112 260 117 131 274 225 222 136 145 97 500
Character W -W -J W e g i v e p r e c i s e d e v e l p
Milliseconds 68 296 125 291 100 144 308 397 231 127 107 40 84 74 240 250 126 66 91 229 132 165 131 92 202
Character -p p -p o p m e n t s o f t h e s e i m p o r
Milliseconds 378 421 329 178 172 204 86 121 17 442 70 82 116 69 170 74 73 193 83 120 98 118 114 150 138
Character t a n t c o n e -e c e p t s i n t - - -t
Milliseconds 183 319 121 51 177 186 51 110 274 402 204 159 97 89 475 102 84 121 104 175 226 224 202 120 136
Character t h e n e x t h -h c h a p t e r , b u t f
Milliseconds 74 98 65 101 290 76 854 171 81 156 393 89 96 84 110 155 152 77 347 166 155 182 24 100 114
Character o r n o w w e u s e a n i n f r o m -m -o
Milliseconds 56 106 43 124 103 25 111 140 205 195 110 133 72 141 147 79 121 204 163 142 192 111 88 241 120
Character -r o r m a l a p p r o c -c a c h s o y o u
Milliseconds 102 170 42 111 109 142 282 257 88 104 97 103 492 262 106 150 107 104 93 78 108 137 113 77 79
Character w i l l s e e h o w t h e y l e a d n a
Milliseconds 73 94 144 126 124 128 87 158 79 119 73 114 92 113 72 83 58 103 118 58 59 167 140 262 68
Character t u r a l l y t o t h e m a i n i d e a
Milliseconds 138 89 101 107 87 111 144 130 112 84 115 171 90 79 53 160 111 37 108 117 93 105 164 86 72
Character o f t h i s c h a p t e r , t h e l i m i
Milliseconds 94 109 82 122 74 104 168 91 150 124 167 115 81 143 77 97 92 101 96 61 103 132 113 133 120
Character n -n t . T h e l i -i -l i d e a o f a l i
Milliseconds 369 331 93 149 98 267 111 76 109 126 221 169 102 130 62 194 95 164 148 117 77 124 126 54 146
Character m i t p l a y a -a - s a f o u n d a t i o
Milliseconds 141 122 96 270 395 185 73 108 111 119 291 105 59 122 115 116 108 188 128 169 86 110 127 10 71
Character n a l r e o l -l -o -e o l e t h r o u g h t o u
Milliseconds 118 155 108 120 195 88 26 156 174 104 107 178 147 34 126 123 66 108 115 100 80 105 81 93 105
Character t -t -u -o -t o u t c a l c u l a -a u s .
Milliseconds 90 193 114 126 114 176 57 81 113 160 130 17 333 312 142 187 337 145 77 140
WPM Timing
Seconds WPM
2.78 64.8
5.56 84.24
8.33 86.4
11.11 84.24
13.89 83.81
16.67 87.12
19.44 82.7
22.22 82.08
25 81.12
27.78 81.65
30.56 84.04
33.33 84.6
36.11 83.41
38.89 84.55
41.67 84.38
44.44 82.62
47.22 81.83
50 82.8
52.78 84.35
55.56 83.81
58.33 82.29
61.11 82.47
63.89 83.4
66.67 82.26
69.44 81.39
72.22 80.42
75 79.52
77.78 80.23
80.56 80.14
83.33 79.92
86.11 78.32
88.89 77.36
91.67 76.97
94.44 75.6
97.22 75.17
100 74.16
102.78 74.61
105.55 74.35
108.33 73.33
111.11 73.44
113.89 73.55
116.67 73.03
119.44 74.04
122.22 74.81
125 75.65
127.78 75.32
130.55 75.28
133.33 75.51
136.11 75.03
138.89 74.65