JGB 🇭🇹 (jgb000)

Race #44581

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Official speed 102.61 wpm (101.04 seconds elapsed during race)
Without ending ping 102.84 wpm (229 ms delay sending score to TypeRacer’s server)
Timerless 102.99 wpm (148 ms elapsed before first character typed; 100.67 seconds elapsed during race)
Timerless minus one 102.87 wpm, ignoring the first character typed
Race Start December 22, 2024 9:42:10pm UTC
Race Finish December 22, 2024 9:43:51pm UTC
Outcome Win (1 of 4)
Accuracy 97.4%
Points 277.05
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 inon one qauanittytity 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 enearly everything we observe in the world and universe, and powerful modern instruments help us se e more and more. In this section we insttduroduce the ideas of abebververage and instanteaangereous rates of change, and hshow that they are closely related to the slope of a curve at a point P on the curse.ve. We give precise developments of these important concepts in the next hacjhaptehapter, but for now we ruse ause an informatll apporroach so you will see how they lead naturally to the main idea of this chapter, the limit. The idea of a limit plays a foundatiotn annal role throughutout calmculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 148 97 116 161 122 138 195 109 90 280 78 71 96 100 65 98 125 180 92 61 77 41 77 28 118
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 25 122 119 93 82 65 91 69 154 129 32 140 95 25 146 79 115 61 99 126 52 80 83 615 117
Character c h a n g e i n o n -n -o o n e q a -a u a n i
Milliseconds 66 82 39 92 69 159 99 37 48 658 37 322 118 67 135 52 104 38 137 352 291 175 52 96 117
Character t t y -y -t -t -i t i t y i s r e l a t e d t o
Milliseconds 0 167 60 291 124 139 140 90 97 96 59 120 114 63 81 305 109 104 104 59 88 177 91 121 120
Character a c h a n g e i n a n o t h e r . H o w
Milliseconds 52 66 147 26 82 53 66 42 88 59 60 45 75 87 64 95 39 93 40 62 103 74 193 90 85
Character d o e s t h e s p e e d o f a f a l l
Milliseconds 77 78 91 72 79 37 82 79 82 78 175 127 72 149 154 69 66 46 77 51 115 38 448 175 134
Character i n g o b j e c t c h a n g e a s a f u
Milliseconds 91 66 85 61 83 80 158 54 193 96 54 135 15 80 38 72 103 39 84 103 69 85 119 76 144
Character n c t i o n o f t i m e ? H o w d o e s
Milliseconds 160 29 79 65 88 62 77 102 32 66 121 101 80 60 222 75 181 107 75 86 107 92 67 55 71
Character t h e l e v e l o f w a t e r i n a b
Milliseconds 74 65 124 51 166 78 121 62 99 100 61 46 68 82 83 62 65 121 69 118 41 68 64 148 122
Character a r r e l c h a n g e a s a f u n c t i o
Milliseconds 90 161 162 86 165 75 128 54 36 87 21 92 83 81 115 86 91 111 33 108 149 73 70 15 123
Character n o f t h e a m o u n t o f l i q u i d
Milliseconds 81 84 63 76 58 123 102 55 114 109 122 90 80 190 106 66 51 150 65 301 44 121 94 77 100
Character p o u r e d i n t o i t ? W e s e e c
Milliseconds 79 155 88 61 107 118 162 74 95 43 69 50 84 136 61 222 62 223 257 130 86 60 202 0 136
Character h a n g e o c c u r r i n g i n e -e n e a r
Milliseconds 83 17 84 41 90 88 221 91 150 119 135 165 98 42 80 63 68 55 80 92 319 135 43 50 53
Character l y e v e r y t h i n g w e o b s e r v e
Milliseconds 61 139 108 215 121 77 116 71 152 48 69 91 55 63 71 83 96 205 42 133 92 26 209 87 78
Character i n t h e w o r l d a n d u n i v e r s e
Milliseconds 54 40 92 79 108 40 76 58 40 66 52 69 73 59 64 85 54 214 118 115 12 87 96 79 49
Character , a n d p o w e r f u l m o d e r n i n s
Milliseconds 121 70 81 57 63 76 60 31 87 66 36 188 80 56 104 134 106 120 148 38 108 80 120 65 73
Character t r u m e n t s h e l p u s s e - e m o
Milliseconds 88 170 84 140 85 66 94 96 80 81 64 94 66 135 99 61 99 113 11 358 350 82 39 53 74
Character r e a n d m o r e . I n t h i s s e c t
Milliseconds 37 74 55 97 76 83 55 49 71 48 67 87 88 216 116 119 61 62 80 81 80 227 132 215 281
Character i o n w e i n s t -t -s t d u -u -d r o d u c e
Milliseconds 90 72 80 103 104 92 95 170 42 72 437 42 158 123 119 143 365 133 52 215 24 697 57 158 38
Character t h e i d e a s o f a b e -e -b b v e r -r -e -v
Milliseconds 103 81 66 46 85 76 127 96 80 116 80 43 80 186 160 209 247 130 148 13 92 105 267 134 134
Character -b v e r a g e a n d i n s t a n t e a -a -e a n
Milliseconds 122 65 124 83 138 124 94 102 135 95 66 51 113 45 56 67 274 113 82 126 201 319 119 57 157
Character g e r -r -e -g e o u s r a t e s o f c h a n g
Milliseconds 25 127 113 331 92 179 72 162 53 71 87 96 120 117 79 96 85 101 67 69 123 63 36 83 35
Character e , a n d h -h s h o w t h a t t h e y a
Milliseconds 72 145 68 80 80 40 75 137 311 115 36 45 93 84 103 56 77 64 60 156 122 67 55 65 132
Character r e c l o s e l y r e l a t e d t o t h e
Milliseconds 105 42 78 149 70 115 95 29 118 134 45 101 67 113 97 62 62 160 59 58 61 78 76 46 88
Character s l o p e o f a c u r v e a t a p o
Milliseconds 38 107 335 169 104 154 86 113 66 60 113 122 208 111 86 209 96 117 162 118 26 162 137 222 56
Character i n t P o n t h e c u r s e . -. -e -s v e .
Milliseconds 58 61 66 50 224 274 307 40 79 93 62 86 23 162 89 68 175 0 251 299 131 122 98 85 66
Character W e g i v e p r e c i s e d e v e l o p m
Milliseconds 129 126 132 38 418 145 69 78 89 182 44 71 185 85 78 82 65 134 116 135 53 119 120 107 176
Character e n t s o f t h e s e i m p o r t a n t c
Milliseconds 112 62 99 60 93 166 63 89 104 81 41 118 86 95 77 102 31 80 31 162 73 39 109 40 146
Character o n c e p t s i n t h e n e x t h a -a -h c
Milliseconds 94 31 105 130 82 93 154 139 122 25 90 23 81 78 47 98 75 164 92 51 161 93 333 123 46
Character j h a p t e -e -t -p -a -h -j h a p t e r , b u t f
Milliseconds 101 10 46 62 106 96 243 142 136 129 133 149 229 50 86 80 88 96 96 58 135 69 116 20 145
Character o r n o w w e r u s e a -a - -e -s -u -r u s e
Milliseconds 47 110 40 53 68 65 52 103 21 133 3 144 66 55 105 105 209 136 126 143 150 126 275 45 35
Character a n i n f o r m a t l -l -t l a p p o r -r -o r
Milliseconds 52 65 78 87 130 47 82 110 49 59 133 65 174 322 107 205 57 53 127 120 161 56 282 110 55
Character o a c h s o y o u w i l l s e e h o w
Milliseconds 133 101 86 73 143 96 83 62 72 83 81 36 123 93 29 161 59 75 60 161 86 77 37 54 88
Character t h e y l e a d n a t u r a l l y t o t h
Milliseconds 61 79 83 63 53 203 25 110 83 103 104 74 85 97 63 94 94 118 150 77 95 120 39 128 86
Character e m a i n i d e a o f t h i s c h a p t
Milliseconds 67 43 126 83 95 24 97 160 42 144 91 37 105 57 56 148 132 68 147 92 162 81 90 24 184
Character e r , t h e l i m i t . T h e i d e a o
Milliseconds 102 91 86 72 82 64 137 41 105 55 121 103 83 132 94 186 121 66 79 67 92 123 80 118 441
Character f a l i m i t p l a y s a f o u n d a t
Milliseconds 58 48 80 121 252 61 100 119 58 75 134 121 38 120 81 71 89 118 112 79 40 164 36 80 51
Character i o t n a -a - -n n -n -t n a l r o l e t h r o
Milliseconds 66 78 15 30 89 69 322 122 137 267 238 114 163 98 4 177 121 117 134 38 71 91 88 111 46
Character u g h u t -t -u o u t c a l m -m c u l u s .
Milliseconds 60 80 92 212 59 331 121 233 37 49 69 140 111 106 328 289 127 152 148 213 107 120
WPM Timing
Seconds WPM
2.02 95.01
4.04 115.79
6.06 108.86
8.08 96.49
10.1 81.95
12.13 87.09
14.15 97.55
16.17 99.46
18.19 102.93
20.21 105.1
22.23 108.5
24.25 110.35
26.27 112.37
28.29 112.4
30.31 111.64
32.33 112.45
34.35 111.78
36.38 113.81
38.4 115.64
40.42 116.09
42.44 115.37
44.46 116.06
46.48 113.86
48.5 110.6
50.52 109.97
52.54 107.57
54.56 106.23
56.58 105.4
58.6 106.07
60.63 106.89
62.65 107.27
64.67 107.07
66.69 106.35
68.71 105.14
70.73 105.36
72.75 106.39
74.77 106.56
76.79 104.07
78.81 104.75
80.83 103.62
82.86 102.4
84.88 102.93
86.9 103.85
88.92 104.46
90.94 105.04
92.96 104.82
94.98 105.5
97 103.92
99.02 103.61
101.04 102.61