Trainer (trainingdiver)

Race #596

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Official speed 105.33 wpm (98.43 seconds elapsed during race)
Without ending ping 105.52 wpm (181 ms delay sending score to TypeRacer’s server)
Timerless 105.87 wpm (318 ms elapsed before first character typed; 97.93 seconds elapsed during race)
Timerless minus one 105.74 wpm, ignoring the first character typed
Race Start March 24, 2024 8:24:28pm UTC
Race Finish March 24, 2024 8:26:07pm UTC
Outcome Win (1 of 3)
Opponents 2. sertouchme (93.74 wpm)
Accuracy 97.3%
Points 284.39
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 hw ow how a change in one quanityi tity is arelate to ad to a hachange in another. How does the speed of a falling object change as a function of time ? How does the fllevel of water in ab arr barrel changes as a function of the amount of liquid poured into it. ? ? We sweee change occurring in nearly everything we observe in the world and universe, and powerful modern intrustruments help us see more and more. In this section we introduce the ideas of averange and instrantaneous eratesrates of change, and wshow that they are closesltlly related to thte sle slope aof a curve at a point P on the curve. We give precise developments of these importnaant concepts in the next chaterpter, but for now we use a n informal approach so you wills 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 a t h
Milliseconds 318 106 95 112 93 157 157 42 68 56 72 68 85 72 60 55 98 121 79 88 57 62 81 89 21
Character e l p s u s u n d e r s t a n d h w - -w -h
Milliseconds 118 99 51 84 72 62 79 92 95 54 54 91 73 138 163 114 114 99 62 90 99 76 193 103 103
Character o w - -w -o h o w a c h a n g e i n o n e
Milliseconds 143 35 57 161 104 109 182 21 41 56 106 87 173 87 63 74 150 219 98 91 44 59 244 71 87
Character q u a n i t y i - -i -y -t -i t i t y i s a -a
Milliseconds 58 97 67 122 24 179 101 46 78 98 110 103 113 118 100 97 91 59 49 43 80 75 238 100 261
Character r e l a t e t o a -a - -o -t - d t o a h a
Milliseconds 82 76 67 82 122 62 60 83 89 33 141 221 94 120 118 132 182 62 149 64 36 96 86 157 93
Character -a -h c h a n g e i n a n o t h e r . H o w
Milliseconds 227 105 178 120 19 108 76 73 80 14 48 98 102 63 29 93 63 51 49 94 87 126 112 32 87
Character d o e s t h e s p e e d o f a f a l l i
Milliseconds 55 109 3 119 132 65 98 57 46 75 88 73 118 116 47 213 89 57 73 102 56 108 32 111 213
Character n g o b j e c t c h a n g e a s a f u n
Milliseconds 36 45 52 64 79 116 33 84 185 69 105 59 62 73 97 70 72 101 46 55 89 87 74 88 132
Character c t i o n o f t i m e - ? H o w d o e s
Milliseconds 45 181 14 57 90 87 104 57 61 102 107 65 15 360 293 254 138 138 105 65 49 72 94 37 124
Character t h e f l -l -f l e v e l o f w a t e r i
Milliseconds 36 85 89 17 73 52 104 163 106 115 84 85 115 138 54 129 44 101 45 75 201 130 32 61 70
Character n a b a r r -r -r -a - -b b a r r e l c h a n
Milliseconds 48 57 84 97 7 128 73 96 122 113 98 127 102 138 105 26 103 102 115 31 134 95 82 58 84
Character g e s -s a s a f u n c t i o n o f t h e
Milliseconds 95 90 145 250 62 106 84 46 99 112 80 124 32 57 143 58 36 104 58 102 69 49 81 79 74
Character a m o u n t o f l i q u i d p o u r e d
Milliseconds 88 73 64 83 766 51 100 59 196 63 50 147 150 91 81 35 76 73 62 141 309 111 123 60 65
Character i n t o i t . - ? - -? -. ? W e s w e -e -w
Milliseconds 103 41 52 85 104 551 50 134 128 196 278 189 201 118 102 212 103 131 142 67 104 136 102 325 96
Character e e c h a n g e o c c u r r i n g i n n e
Milliseconds 192 117 102 80 84 37 84 78 71 60 82 44 244 216 90 142 133 29 73 59 41 67 62 129 91
Character a r l y e v e r y t h i n g w e o b s e r v
Milliseconds 91 59 123 78 51 83 133 152 65 75 82 68 82 91 50 76 97 31 77 50 69 100 134 45 144
Character e i n t h e w o r l d a n d u n i v e r
Milliseconds 121 71 86 23 98 67 101 42 58 83 85 51 84 76 91 56 110 58 70 81 118 52 57 142 64
Character s e , a n d p o w e r f u l m o d e r n i
Milliseconds 99 39 222 64 120 127 42 60 110 117 66 23 160 144 63 151 120 55 56 59 52 82 103 69 60
Character n t r u -u -r -t s t r u m e n t s h e l p u s
Milliseconds 52 42 93 149 218 113 114 112 78 56 93 132 84 84 69 96 64 55 102 94 55 113 104 69 73
Character s e e m o r e a n d m o r e . I n t h i
Milliseconds 140 124 133 107 10 92 72 78 140 82 111 59 50 56 53 56 23 132 76 152 137 517 113 60 50
Character s s e c t i o n w e i n t r o d u c e t h
Milliseconds 53 50 114 56 128 167 30 23 114 50 63 19 113 38 57 185 80 56 119 85 51 117 69 79 68
Character e i d e a s o f a v e r a n -n g e a n d
Milliseconds 46 77 92 51 126 97 78 38 110 51 52 83 146 129 43 104 108 406 39 111 83 76 69 60 47
Character i n s t r -r a n t a n e o u s e r a t e s -s -e -t
Milliseconds 60 40 77 151 116 440 61 115 57 228 81 152 89 130 98 72 214 6 99 99 95 132 290 121 123
Character -a -r -e r a t e s o f c h a n g e , a n d w
Milliseconds 117 124 131 112 108 103 103 108 71 103 68 53 96 105 37 111 56 86 61 106 87 62 73 53 155
Character -w s h o w t h a t t h e y a r e c l o s e
Milliseconds 246 109 93 35 43 69 87 78 41 74 69 49 72 99 44 92 73 68 84 53 131 53 137 43 123
Character s l t -t -l l -l -s l y r e l a t e d t o t h t
Milliseconds 95 65 118 209 114 233 160 111 141 70 50 139 56 116 46 124 105 21 125 93 100 71 32 236 15
Character e s l -l -s - -e -t e s l o p e a -a o f a c
Milliseconds 90 63 109 16 207 110 109 115 110 73 68 77 66 138 81 32 72 364 227 138 66 65 57 117 43
Character u r v e a t a p o i n t P o n t h e
Milliseconds 127 68 109 103 75 92 95 70 48 95 632 122 116 159 80 55 139 72 128 42 62 128 23 72 62
Character c u r v e . W e g i v e p r e c i s e d e
Milliseconds 99 95 49 117 102 69 84 137 127 70 147 66 67 99 70 115 58 53 190 133 106 175 70 97 55
Character v e l o p m e n t s o f t h e s e i m p o r
Milliseconds 136 100 76 134 73 103 42 115 65 151 48 85 83 45 106 85 47 133 140 74 55 134 44 128 67
Character t n a -a -n a n t c o n c e p t s i n t h e
Milliseconds 52 428 19 324 106 114 76 68 59 108 57 44 51 120 84 56 109 80 96 34 69 78 95 46 73
Character n e x t c h a t e r -r -e -t p t e r , b u t f
Milliseconds 114 35 138 190 57 90 108 38 204 108 49 277 95 122 238 84 99 17 91 95 85 64 56 62 189
Character o r n o w w e u s e a - n i n f o r m
Milliseconds 35 111 136 78 27 412 76 102 19 131 110 74 123 87 80 147 444 302 143 148 41 118 97 68 107
Character a l a p p r o a c h s o y o u w i l l s
Milliseconds 86 140 105 144 105 95 134 86 32 115 73 70 189 103 98 74 46 99 53 28 94 147 97 236 211
Character - -s s e e h o w t h e y l e a d n a t u
Milliseconds 194 98 92 56 131 131 92 80 32 59 52 113 65 54 92 62 297 66 117 73 212 132 51 108 105
Character r a l l y t o t h e m a i n i d e a o f
Milliseconds 18 105 90 88 85 64 127 90 86 524 245 53 79 45 111 110 69 81 121 29 137 24 198 114 77
Character t h i s c h a p t e r , t h e l i m i t .
Milliseconds 43 122 37 36 68 63 119 81 32 148 42 95 27 123 53 80 81 36 64 97 132 172 116 83 151
Character T h e i d e a o f a l i m i t p l a y
Milliseconds 135 200 71 67 62 77 73 129 67 104 100 78 46 88 88 42 137 134 72 58 81 123 65 109 126
Character s a f o u n d a t i o n a l r o l e t h r
Milliseconds 39 98 42 108 64 41 157 49 41 93 99 31 24 682 73 125 73 66 93 108 93 45 161 142 99
Character o u g h o u t c a l c u l u s .
Milliseconds 69 117 103 42 206 134 74 55 134 109 84 62 101 130 148 61 95
WPM Timing
Seconds WPM
1.97 115.81
3.94 128.01
5.91 101.59
7.87 103.62
9.84 93.87
11.81 87.37
13.78 90.56
15.75 96.77
17.72 102.27
19.69 106.67
21.66 105.29
23.62 105.15
25.59 102.22
27.56 103.62
29.53 102.81
31.5 104
33.47 98.96
35.44 96.85
37.4 98.81
39.37 100.88
41.34 103.62
43.31 104.73
45.28 104.15
47.25 105.66
49.22 105.82
51.19 107.61
53.15 107.69
55.12 106.24
57.09 104.04
59.06 104.84
61.03 104.8
63 104.58
64.97 102.88
66.93 102.73
68.9 103.45
70.87 103.79
72.84 104.45
74.81 104.1
76.78 104.25
78.75 104.08
80.72 103.03
82.68 103.48
84.65 102.91
86.62 103.35
88.59 103.22
90.56 104.29
92.53 104.53
94.5 105.4
96.46 105.24
98.43 105.33