+ (doublestab)

Race #1594

View Pit Stop page for race #1594 by doublestab — Ghost race

View profile for + (doublestab)

Official speed 117.02 wpm (88.60 seconds elapsed during race)
Without ending ping 117.57 wpm (412 ms delay sending score to TypeRacer’s server)
Timerless 117.96 wpm (294 ms elapsed before first character typed; 87.89 seconds elapsed during race)
Timerless minus one 117.82 wpm, ignoring the first character typed
Race Start December 5, 2023 12:12:02pm UTC
Race Finish December 5, 2023 12:13:30pm UTC
Outcome No win (2 of 5)
Opponents 1. lhykv (166.02 wpm)
Accuracy 98.3%
Points 315.96
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 tht at helps us understndand how a change in one quantity is related to a change in another. how How does the speed of a falling objetcct change as a function of time? howHow does the level of water in a barrel change as a function of the amount of liquid poured into it? We see change occurring i nnn nearly everything we observe in the world and universe, and powerful modern instruments help us see more and more. In theis 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 oipoint P on the curve. We give precise developemtmments of these mumpimprotortant concepts in the next chapter, but for now wew u use an informal aprproach 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.
Timing
Character C a l c u l u s i s a t o o l t h t - -t
Milliseconds 294 99 112 87 103 358 203 82 51 71 78 74 60 103 49 56 131 140 53 39 96 123 63 272 121
Character a t h e l p s u s u n d e r s t n d -d -n a n
Milliseconds 54 47 65 52 91 81 159 56 81 64 66 87 118 176 62 67 60 148 65 142 146 232 112 35 150
Character d h o w a c h a n g e i n o n e q u a
Milliseconds 53 72 56 151 73 88 58 115 233 88 92 56 55 135 0 97 128 36 114 149 35 114 104 40 153
Character n t i t y i s r e l a t e d t o a c h a
Milliseconds 56 90 82 44 124 35 79 74 66 72 108 65 74 78 142 99 96 65 93 45 100 97 55 93 69
Character n g e i n a n o t h e r . h o w - -w -o -h H
Milliseconds 71 64 119 20 67 160 47 20 58 135 86 93 44 61 74 70 175 143 46 101 186 148 122 162 210
Character o w d o e s t h e s p e e d o f a f a
Milliseconds 144 41 102 51 98 40 74 77 73 84 51 96 56 316 64 122 126 111 0 93 87 69 93 59 77
Character l l i n g o b j e t c -c -t c t c h a n g e a
Milliseconds 51 136 184 184 43 68 144 260 162 65 247 176 72 172 46 134 47 124 25 134 37 62 140 59 90
Character s a f u n c t i o n o f t i m e ? h o w
Milliseconds 50 80 71 104 65 252 144 43 138 54 136 72 70 72 90 49 91 36 158 97 260 71 150 183 53
Character -w -o -h H o w d o e s t h e l e v e l o f
Milliseconds 196 120 128 141 151 100 89 56 95 49 110 48 73 89 66 50 91 44 167 50 156 31 248 21 209
Character w a t e r i n a b a r r e l c h a n g e
Milliseconds 47 76 133 90 50 91 293 149 38 55 132 53 75 81 122 151 43 78 41 124 17 144 94 121 49
Character a s a f u n c t i o n o f t h e a m o u
Milliseconds 51 104 101 112 79 53 56 155 34 91 93 137 16 117 52 112 70 49 70 81 52 70 72 159 172
Character n t o f l i q u i d p o u r e d i n t o
Milliseconds 140 70 51 92 112 35 43 171 71 96 116 63 57 76 161 159 126 115 123 23 49 157 72 72 88
Character i t ? W e s e e c h a n g e o c c u r r i
Milliseconds 138 79 189 48 80 169 103 181 167 120 111 50 85 87 93 55 133 39 89 96 111 144 85 155 69
Character n g i n n -n -n - n n e a r l y e v e r y t
Milliseconds 131 45 56 111 161 0 212 231 122 125 196 40 111 59 43 88 73 89 71 73 102 113 38 133 56
Character h i n g w e o b s e r v e i n t h e w o
Milliseconds 103 138 139 53 83 65 38 58 87 168 47 54 132 95 108 76 56 167 43 21 81 53 67 47 98
Character r l d a n d u n i v e r s e , a n d p o w
Milliseconds 68 78 77 65 71 59 85 48 65 136 154 33 83 48 105 80 63 63 74 98 62 61 71 133 44
Character e r f u l m o d e r n i n s t r u m e n t s
Milliseconds 36 159 144 36 134 78 121 136 20 82 45 98 88 179 249 43 108 111 32 138 54 96 23 128 55
Character h e l p u s s e e m o r e a n d m o r e
Milliseconds 50 116 69 160 37 116 80 71 71 113 117 82 52 156 45 43 82 94 45 93 30 72 180 36 24
Character . I n t h e -e i s s e c t i o n w e i n
Milliseconds 80 99 140 151 44 39 79 72 247 153 81 83 52 74 138 144 28 137 63 100 63 48 80 199 115
Character t r o d u c e t h e i d e a s o f a v e r
Milliseconds 67 134 28 106 57 76 112 64 109 34 87 27 59 74 130 59 77 127 57 124 61 161 174 115 45
Character a g e a n d i n s t a n t a n e o u s r a t
Milliseconds 104 103 75 54 82 61 81 40 72 153 78 136 118 76 54 257 171 108 105 161 80 47 55 105 87
Character e s o f c h a n g e , a n d s h o w t h
Milliseconds 128 120 63 41 89 64 81 86 59 106 68 122 36 81 41 124 47 140 80 105 151 41 99 43 122
Character a t t h e y a r e c l o s e l y r e l a t
Milliseconds 27 93 49 94 31 141 0 79 39 41 114 68 84 50 155 34 52 71 112 42 86 106 120 71 116
Character e d t o t h e s l o p e o f a c u r v
Milliseconds 124 105 103 74 43 93 43 68 72 39 101 59 137 139 60 68 48 76 89 48 96 56 87 53 142
Character e a t a o i -i -o p o i n t P o n t h e
Milliseconds 70 119 53 82 109 54 74 273 176 305 114 129 142 351 174 69 91 191 134 207 169 51 49 48 91
Character c u r v e . W e g i v e p r e c i s e d
Milliseconds 32 97 48 79 158 55 68 71 135 148 97 89 100 88 167 41 50 54 103 127 105 344 128 125 84
Character e v e l o p e m t -t -m m -m -e m e n t s o f t h
Milliseconds 122 123 109 62 146 175 126 60 142 194 140 146 219 148 161 51 116 13 127 32 58 102 88 55 84
Character e s e m -m u m p -p -m -u i m p r o t -t -o -r o r t a
Milliseconds 53 76 106 78 207 255 189 157 257 114 174 113 150 150 143 133 0 141 201 102 182 71 68 44 134
Character n t c o n c e p t s i n t h e n e x t c
Milliseconds 136 57 118 71 66 158 0 89 110 97 144 52 69 159 39 34 86 46 43 80 14 137 136 55 99
Character h a p t e r , b u t f o r n o w w e w u
Milliseconds 44 71 125 33 115 56 67 41 137 52 94 60 90 39 81 77 46 125 50 93 44 35 76 101 81
Character -u - -w u s e a n i n f o r m a l a p r -r p
Milliseconds 250 98 143 46 107 84 47 69 91 60 48 130 115 67 76 64 83 54 87 36 60 81 170 357 130
Character r o a c h s o y o u w i l l s e e h o w
Milliseconds 62 88 49 75 122 145 144 156 71 54 53 82 54 107 28 151 112 51 17 44 128 76 52 163 45
Character t h e y l e a d n a t u r a l l y t o t
Milliseconds 101 11 126 38 105 37 157 38 44 87 40 69 80 84 91 45 87 76 121 98 70 125 170 152 47
Character h e m a i n i d e a o f t h i s c h a p
Milliseconds 88 78 40 52 90 75 115 20 132 61 99 56 71 47 76 78 121 52 150 57 83 46 76 75 103
Character t e r , t h e l i m i t . T h e i d e a
Milliseconds 41 124 52 48 108 44 108 60 84 176 186 118 151 81 96 64 161 159 68 88 80 60 127 78 34
Character o f a l i m i t p l a y s a f o u n d a
Milliseconds 89 65 64 71 72 80 146 136 158 85 59 71 145 71 116 132 90 80 65 70 43 178 107 28 60
Character t i o n a l r o l e t h r o u g h o u t c a
Milliseconds 90 51 131 131 49 100 52 76 87 126 71 68 88 128 64 93 155 91 47 137 127 70 48 99 58
Character l c u l u s .
Milliseconds 47 93 95 128 172 60 72
WPM Timing
Seconds WPM
1.77 88.04
3.54 98.19
5.32 92.55
7.09 103.27
8.86 111.06
10.63 118.51
12.4 108.35
14.18 110.89
15.95 108.35
17.72 108.35
19.49 108.97
21.26 106.09
23.04 106.79
24.81 108.84
26.58 111.51
28.35 111.74
30.12 111.94
31.9 112.49
33.67 110.49
35.44 111.74
37.21 113.83
38.98 115.12
40.76 115.71
42.53 116.82
44.3 116.48
46.07 117.47
47.84 117.88
49.62 117.78
51.39 118.63
53.16 120.09
54.93 120.8
56.7 121.26
58.48 118.82
60.25 118.91
62.02 118.61
63.79 116.25
65.56 115.86
67.34 113.34
69.11 113.21
70.88 114.28
72.65 113.97
74.42 113.83
76.2 114.49
77.97 115.43
79.74 116.03
81.51 116.6
83.28 116.71
85.06 116.82
86.83 117.2
88.6 117.02