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Race #114265

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Official speed 110.96 wpm (93.44 seconds elapsed during race)
Without ending ping 111.36 wpm (224 ms delay sending score to TypeRacer’s server)
Timerless 111.72 wpm (307 ms elapsed before first character typed; 92.91 seconds elapsed during race)
Timerless minus one 111.59 wpm, ignoring the first character typed
Race Start October 3, 2023 12:12:02pm UTC
Race Finish October 3, 2023 12:13:36pm UTC
Outcome No win (2 of 4)
Opponents 3. jahed100 (105.57 wpm)
4. accuracy_acc (98.08 wpm)
Accuracy 98.0%
Points 299.60
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 changei n in one quantity is related to a change in another. How does the speped of a falling object change as a function of time? How dieoes the level of water in a barrel change as a function of the maamount of liquid poured into ti? it? We see change occuring in ccurring in nearly everything we observe n thein the e wworld and univeresse, and powerful modern instruments help us see more and more. In this section we indtroduce the ideas of average and instanctaneous 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 informanl papproach so you will se e how they lead naturally to the main idea of this chapter, the limit. The idea of a limit plays a foundational role throughout clalculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 307 204 192 235 59 121 226 127 43 41 104 32 124 48 78 55 125 156 72 39 35 80 19 60 179
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 94 107 130 96 93 101 65 70 418 99 53 144 27 135 124 81 0 115 39 79 43 47 60 182 75
Character c h a n g e i n -n - -i i n o n e q u a n t
Milliseconds 126 87 78 21 67 36 55 66 14 484 143 134 60 113 58 52 95 73 33 58 268 61 123 43 127
Character i t y i s r e l a t e d t o a c h a n g
Milliseconds 55 117 51 67 67 103 10 153 60 46 79 181 69 102 30 101 46 92 66 104 74 141 130 57 32
Character e i n a n o t h e r . H o w d o e s t h
Milliseconds 57 69 45 46 76 188 4 129 75 79 23 78 87 45 185 112 66 43 479 110 7 81 184 168 76
Character e s p e p -p e d o f a f a l l i n g o b
Milliseconds 44 96 177 56 114 52 393 92 111 54 97 62 36 100 118 238 47 79 104 97 48 56 33 147 109
Character j e c t c h a n g e a s a f u n c t i o n
Milliseconds 88 88 168 136 125 111 24 602 131 86 8 81 183 321 127 78 67 169 107 101 61 119 91 73 53
Character o f t i m e ? H o w d i e -e -i o e s t h
Milliseconds 53 94 36 42 102 55 57 69 320 21 205 126 68 75 138 122 63 298 118 149 51 45 57 78 91
Character e l e v e l o f w a t e r i n a b a r
Milliseconds 43 84 111 53 149 33 104 94 167 84 103 196 178 39 55 99 25 58 57 77 301 118 127 98 92
Character r e l c h a n g e a s a f u n c t i o n
Milliseconds 134 31 70 82 237 37 523 136 65 21 79 160 158 93 61 47 76 113 208 134 128 38 43 56 56
Character o f t h e m a -a -m a m o u n t o f l i q u
Milliseconds 90 34 44 90 34 68 69 152 27 418 125 88 82 42 101 129 20 109 55 45 33 128 53 181 97
Character i d p o u r e d i n t o t i ? - -? -i -t i t
Milliseconds 38 115 93 248 121 108 209 97 384 115 194 94 45 42 83 76 26 261 55 227 145 135 280 215 65
Character ? W e s e e c h a n g e o c c u r i n g
Milliseconds 355 128 183 152 111 146 84 129 46 146 48 79 55 53 36 84 274 95 135 96 78 73 93 30 45
Character i n -c -c -u -r -i -n -g - -i -n - c c u r r i n g i n
Milliseconds 81 44 78 734 0 0 0 0 0 0 0 0 0 0 136 128 32 133 109 71 40 69 30 105 42
Character n e a r l y e v e r y t h i n g w e o b s
Milliseconds 47 221 98 67 42 129 95 34 236 154 59 86 64 76 44 59 91 30 46 55 83 54 196 131 106
Character e r v e n t h e $i - -t -h -e n t h e e w -w
Milliseconds 49 35 169 57 69 204 102 78 77 42 680 0 0 0 0 39 84 42 91 69 166 11 289 101 222
Character - -e w o r l d a n d u n i v e r e s -s -e s e ,
Milliseconds 122 169 90 115 88 41 119 82 111 16 103 31 139 122 85 18 90 112 97 10 480 102 48 47 98
Character a n d p o w e r f u l m o d e r n i n s t
Milliseconds 91 14 55 55 49 101 70 50 15 88 137 42 132 76 286 5 92 119 56 55 119 77 104 18 87
Character r u m e n t s h e l p u s s e e m o r e
Milliseconds 125 59 128 92 72 20 114 43 106 91 76 165 137 104 115 141 68 129 158 93 38 18 74 27 58
Character a n d m o r e . I n t h i s s e c t i o n
Milliseconds 113 56 45 32 96 41 35 31 116 31 493 151 81 77 43 45 90 45 128 51 166 111 30 18 69
Character w e i n d -d t r o d u c e t h e i d e a s
Milliseconds 67 119 49 153 225 98 68 295 72 119 65 151 87 119 131 90 26 57 55 70 89 102 105 96 85
Character o f a v e r a g e a n d i n s t a n c -c t
Milliseconds 89 147 76 64 244 169 63 147 107 85 65 73 52 100 80 10 206 105 80 108 94 59 96 328 44
Character a n e o u s r a t e s o f c h a n g e , a
Milliseconds 61 341 58 72 96 20 93 245 50 131 30 108 27 80 77 24 159 91 51 69 43 37 89 58 53
Character n d s h o w t h a t t h e y a r e c l o
Milliseconds 68 55 47 170 86 46 82 84 62 55 104 67 4 107 33 103 11 99 90 68 57 35 137 50 114
Character s e l y r e l a t e d t o t h e s l o p e
Milliseconds 24 32 140 82 48 115 78 107 80 90 52 117 3 120 36 73 51 70 35 88 126 45 125 189 34
Character o f a c u r v e a t a p o i n t P
Milliseconds 275 167 50 12 128 109 107 107 43 268 38 92 102 65 86 123 63 130 13 66 144 28 143 207 114
Character o n t h e c u r v e . W e g i v e p r e
Milliseconds 87 42 56 92 91 57 80 163 83 56 208 48 187 61 241 177 67 163 50 153 19 77 80 321 64
Character c i s e d e v e l o p m e n t s o f t h e s
Milliseconds 155 44 133 45 86 139 132 134 40 72 134 286 214 128 117 29 141 215 183 71 114 98 41 80 182
Character e i m p o r t a n t c o n c e p t s i n t
Milliseconds 32 57 158 64 103 0 55 158 47 155 199 127 169 80 144 212 191 38 119 63 83 25 59 66 56
Character h e n e x t c h a p t e r , b u t f o r
Milliseconds 69 58 66 94 50 166 117 46 271 33 133 46 97 60 71 92 50 145 28 138 4 163 32 122 23
Character n o w w e u s e a n i n f o r m a n -n l
Milliseconds 91 31 46 59 99 91 57 126 63 81 56 131 45 84 144 23 65 89 63 120 105 115 401 184 100
Character p -p a p p r o a c h s o y o u w i l l s e
Milliseconds 241 238 89 122 130 78 114 113 145 38 97 168 39 106 42 37 89 53 57 67 128 110 44 57 102
Character - e h o w t h e y l e a d n a t u r a l
Milliseconds 196 353 90 67 141 20 52 56 81 93 64 37 79 194 99 69 122 63 230 78 105 110 122 52 59
Character l y t o t h e m a i n i d e a o f t h
Milliseconds 119 75 51 125 28 85 69 43 43 82 113 54 107 101 90 119 90 141 20 129 110 96 10 267 60
Character i s c h a p t e r , t h e l i m i t . T h
Milliseconds 55 46 79 129 50 82 98 67 56 68 73 75 116 31 65 54 83 65 121 48 188 167 146 169 226
Character e i d e a o f a l i m i t p l a y s a
Milliseconds 95 94 124 78 125 5 131 125 38 46 65 89 327 68 101 84 97 26 107 147 62 94 87 88 80
Character f o u n d a t i o n a l r o l e t h r o u g
Milliseconds 89 52 104 119 47 135 303 161 68 98 68 44 142 68 38 95 116 26 67 67 93 99 22 57 56
Character h o u t c l -l a l c u l u s .
Milliseconds 83 76 101 25 91 151 109 405 87 166 92 69 185 121 76 78
WPM Timing
Seconds WPM
1.87 89.9
3.74 105.95
5.61 115.58
7.48 105.95
9.34 114.3
11.21 119.86
13.08 113.75
14.95 114.78
16.82 110.59
18.69 112.37
20.56 109.75
22.43 111.3
24.29 108.67
26.16 111
28.03 110.02
29.9 107.96
31.77 104.25
33.64 104.17
35.51 99.36
37.38 100.81
39.24 102.74
41.11 99.82
42.98 99.95
44.85 100.33
46.72 101.97
48.59 103.73
50.46 104.41
52.33 104.12
54.19 104.51
56.06 104.02
57.93 105.64
59.8 107.56
61.67 108.38
63.54 108.97
65.41 109.16
67.28 108.98
69.14 108.47
71.01 108.66
72.88 109.16
74.75 110.13
76.62 110.1
78.49 109.16
80.36 109.31
82.23 109.75
84.1 110.45
85.96 111.12
87.83 111.07
89.7 111.3
91.57 111.91
93.44 110.96