Nikola (dropndrag)

Race #8238

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Official speed 79.71 wpm (130.07 seconds elapsed during race)
Without ending ping 79.82 wpm (178 ms delay sending score to TypeRacer’s server)
Timerless 80.01 wpm (306 ms elapsed before first character typed; 129.59 seconds elapsed during race)
Timerless minus one 79.91 wpm, ignoring the first character typed
Race Start December 22, 2023 10:12:52am UTC
Race Finish December 22, 2023 10:15:02am UTC
Outcome Win (1 of 2)
Accuracy 96.2%
Points 215.22
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 chang e in on quane quantity is related to a change in another. How does the seppeed of a falling obgectject chang ae as a unuufunction of time? How daoes the leverl of water in a barrel change as a ufnfufunction of the amount of liquitd pourned into it? We see change occurring in neraarly everything we obrvseserve in the world and unviiverse ,, and powerful modern instruments help us see more and omemore. In this section we introduce the ideas of evaverage iaand instantaneous rates of chang, ae, and show that they are closeliy relatetd d tothe the slope of a cureve at a point P on the curve. We give precise developments of these important concept in s i n the next chapter, but for now we use an informal aprproach so you will see how they lead naturally to the main inedea of this scaptphapter, the litimit. The idea of a litmit plays , a foundational role throughout caluculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 306 190 178 210 128 145 123 174 145 120 54 73 143 99 90 122 128 116 81 115 57 78 77 85 134
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 90 99 266 130 121 406 145 92 867 82 232 91 122 142 54 117 80 138 104 124 98 53 114 156 96
Character c h a n g - e i n o n q u a n -n -a -u -q - e
Milliseconds 74 22 70 115 128 147 413 123 116 103 68 225 106 88 123 128 17 117 84 234 210 155 146 201 189
Character q u a n t i t y i s r e l a t e d t o a
Milliseconds 128 75 54 73 141 120 98 168 218 127 171 101 63 114 92 144 90 112 132 105 115 100 105 97 242
Character c h a n g e i n a n o t h e r . H o w d
Milliseconds 116 104 96 27 143 166 99 122 103 49 117 79 99 91 98 109 69 114 105 102 125 116 95 81 76
Character o e s t h e s e p -p -e p e e d o f a f a
Milliseconds 167 270 217 121 217 47 99 81 111 70 158 458 131 190 93 148 104 134 31 76 143 117 109 122 92
Character l l i n g o b g e c t -t -c -e -g j e c t c h a n
Milliseconds 97 175 71 120 75 95 74 121 104 128 81 135 261 116 131 126 111 123 46 81 116 84 44 74 122
Character g a -a - e a s a u n u -u -n -u u -u f u n c t
Milliseconds 67 123 160 304 108 190 140 99 122 84 73 173 0 86 153 288 106 162 225 396 168 74 123 166 101
Character i o n o f t i m e ? H o w d a -a o e s t
Milliseconds 102 76 70 95 94 73 94 28 120 76 51 224 147 127 253 154 114 97 164 454 125 113 127 103 74
Character h e l e v e r -r l o f w a t e r i n a
Milliseconds 67 84 72 139 104 109 98 151 374 82 98 73 80 105 117 54 171 169 238 115 97 98 83 101 114
Character b a r r e l c h a n g e a s a u f n -n -f f
Milliseconds 43 104 49 166 80 127 98 110 28 69 107 91 148 143 124 107 90 99 169 67 226 4 208 220 185
Character u -u -f -u f u n c t i o n o f t h e a m o u n
Milliseconds 113 195 127 143 175 65 133 133 58 116 32 114 104 92 73 117 25 103 80 328 158 118 285 102 175
Character t o f l i q u i t -t d p o u r n -n e d i n
Milliseconds 264 147 99 95 92 79 101 186 102 123 365 268 101 73 74 115 54 124 151 382 170 99 98 98 73
Character t o i t ? W e s e e c h a n g e o c c u
Milliseconds 97 102 184 104 74 127 136 137 139 71 121 127 142 22 149 29 69 121 96 104 118 69 125 166 83
Character r r i n g i n n e r a -a -r a r l y e v e r y
Milliseconds 92 222 163 107 93 78 122 89 127 103 94 153 47 293 122 146 60 206 129 82 150 98 123 49 121
Character t h i n g w e o b r v s e -e -s -v -r s e r v e
Milliseconds 107 113 147 42 124 77 268 73 79 258 112 291 212 52 71 174 124 136 223 124 119 97 167 85 391
Character i n t h e w o r l d a n d u n v i -i -v i v
Milliseconds 90 121 72 75 68 75 55 49 99 113 222 78 81 171 113 179 134 101 77 193 123 315 124 96 123
Character e r s e , -, - , a n d p o w e r f u l m o
Milliseconds 120 123 146 151 363 146 224 116 197 98 96 81 58 79 76 80 75 97 114 99 105 116 94 179 99
Character d e r n i n s t r u m e n t s h e l p u s
Milliseconds 137 70 152 99 97 220 78 163 118 71 104 93 97 61 118 115 102 50 66 99 136 97 114 103 91
Character s e e m o r e a n d o m e -e -m -o m o r e .
Milliseconds 127 90 135 84 85 115 106 91 76 123 93 74 73 116 12 256 250 101 122 240 98 197 48 140 185
Character I n t h i s s e c t i o n w e i n t r o d
Milliseconds 65 204 88 99 98 91 74 78 130 91 130 98 122 45 102 96 96 97 94 74 100 96 74 342 105
Character u c e t h e i d e a s o f e v -v -e a v e r
Milliseconds 145 117 163 109 51 100 90 75 148 219 196 97 230 120 113 97 94 104 145 263 122 129 74 105 117
Character a g e i a -a -i a n d i n s t a n t a n e o u s
Milliseconds 97 96 104 117 97 44 279 110 204 79 68 88 82 114 105 55 116 77 126 254 128 97 202 116 116
Character r a t e s o f c h a n g , a -a - -, e , a
Milliseconds 109 78 114 90 106 144 202 183 61 117 127 41 51 115 88 138 121 123 222 118 124 272 138 123 97
Character n d s h o w t h a t t h e y a r e c l o
Milliseconds 96 53 97 171 78 91 590 121 68 55 75 83 99 123 58 142 57 113 26 163 97 82 99 118 140
Character s e l i -i y r e l a t e t d - -d -t d t o t h
Milliseconds 103 105 146 141 508 464 97 122 66 124 86 90 141 154 0 71 321 120 145 123 122 80 91 144 142
Character e -e -h -t t h e s l o p e o f a c u r e -e
Milliseconds 103 324 121 115 268 68 109 92 101 160 200 74 97 145 228 84 103 98 117 127 74 92 86 364 524
Character v e a t a p o i n t P o n t h e c u
Milliseconds 102 100 118 106 145 93 124 118 17 103 179 319 156 202 93 272 147 99 122 96 29 69 89 56 98
Character r v e . W e g i v e p r e c i s e d e v e
Milliseconds 68 154 115 176 117 127 102 143 106 89 166 317 101 99 99 103 94 166 124 138 104 104 66 149 75
Character l o p m e n t s o f t h e s e i m p o r t a
Milliseconds 150 123 108 218 84 87 106 169 76 48 96 97 27 96 76 72 97 29 118 103 43 107 84 86 114
Character n t c o n c e p t i n - -n -i - s i - n
Milliseconds 68 81 97 100 71 79 139 69 83 117 142 98 77 145 270 219 149 139 132 99 111 151 415 147 105
Character t h e n e x t c h a p t e r , b u t f o r
Milliseconds 82 79 82 77 115 94 128 287 224 336 48 98 127 143 141 302 117 144 59 94 77 109 80 98 97
Character n o w w e u s e a n i n f o r m a l a
Milliseconds 96 225 99 124 96 379 109 117 127 100 93 90 101 77 95 145 348 168 97 77 115 107 499 127 152
Character p r -r p r o a c h s o y o u w i l l s e e
Milliseconds 142 146 415 140 133 150 82 149 104 291 271 80 85 128 29 94 31 121 140 98 197 51 120 96 173
Character h o w t h e y l e a d n a t u r a l l y
Milliseconds 197 122 89 101 99 98 97 82 94 80 88 66 99 134 117 192 102 80 120 118 79 134 177 101 69
Character t o t h e m a i n i n e -e -n d e a o f t
Milliseconds 79 75 116 90 81 82 67 99 69 177 92 50 273 135 72 318 120 136 72 96 99 145 89 84 64
Character h i s s -s c a p t -t -p -a p -p h a p t e r , t h
Milliseconds 79 116 79 44 122 331 110 70 99 153 286 120 154 152 452 295 105 98 124 120 145 240 106 59 57
Character e l i t i -i -t m i t . T h e i d e a o f
Milliseconds 70 76 70 78 126 213 272 125 123 114 608 145 170 127 121 77 84 81 129 115 81 171 40 123 128
Character a l i t -t m i t p l a y s , - -, a f o u
Milliseconds 600 141 226 104 132 443 170 103 337 122 97 122 128 98 188 73 123 407 171 122 176 107 89 121 97
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 92 177 146 116 103 99 66 129 147 97 117 79 139 60 119 65 204 191 99 47 69 126 171 72 179
Character c a l u -u c u l u s .
Milliseconds 116 121 116 196 152 445 231 102 140 84 241 141
WPM Timing
Seconds WPM
2.6 83.03
5.2 76.11
7.8 84.57
10.41 71.5
13.01 76.57
15.61 83.03
18.21 80.4
20.81 81.88
23.41 78.93
26.01 75.65
28.62 76.32
31.22 77.65
33.82 80.55
36.42 78.09
39.02 78.73
41.62 77.84
44.22 79.78
46.83 79.44
49.43 79.63
52.03 79.34
54.63 78.86
57.23 78.84
59.83 80.22
62.43 79.96
65.04 81.37
67.64 81.61
70.24 80.98
72.84 81.55
75.44 81.28
78.04 81.95
80.64 80.65
83.25 79.86
85.85 79.54
88.45 80.05
91.05 80.4
93.65 81.62
96.25 81.16
98.85 80.85
101.46 81.02
104.06 81.07
106.66 80.78
109.26 81.49
111.86 82.17
114.46 81.67
117.06 80.98
119.67 80.52
122.27 79.99
124.87 79.57
127.47 80.11
130.07 79.71