Sebastian (4555)

Race #6676

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Official speed 111.07 wpm (93.35 seconds elapsed during race)
Without ending ping 111.23 wpm (137 ms delay sending score to TypeRacer’s server)
Timerless 112.38 wpm (951 ms elapsed before first character typed; 92.26 seconds elapsed during race)
Timerless minus one 112.25 wpm, ignoring the first character typed
Race Start December 30, 2024 2:57:41am UTC
Race Finish December 30, 2024 2:59:14am UTC
Outcome Win (1 of 3)
Opponents 2. shudd3r (79.92 wpm)
Accuracy 98.9%
Points 299.90
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 in one quantitity 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 an dund 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 scurve at a point P on the curve. We give precise developments of these important concepts in the next chapter, but for now swe use an informal papapproach so you will see how they lead naturally to the main idea of this chapter, the limit. The ideao f 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 951 238 144 126 404 264 71 183 85 73 112 47 125 58 129 112 128 131 106 112 50 82 41 38 190
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 140 34 105 91 119 123 71 73 135 153 81 162 50 150 84 100 65 81 125 97 39 61 75 105 54
Character c h a n g e i n o n e q u a n t i t i -i -t t
Milliseconds 125 38 130 88 103 67 43 93 45 78 93 81 48 70 213 67 155 77 177 70 226 36 445 123 482
Character y i s r e l a t e d t o a c h a n g e
Milliseconds 71 176 253 37 102 142 61 97 145 30 97 145 85 75 21 105 64 115 112 83 93 70 57 60 95
Character i n a n o t h e r . H o w d o e s t h e
Milliseconds 45 69 64 73 105 74 69 147 21 83 127 109 521 199 45 116 152 60 96 82 84 102 25 51 91
Character s p e e d o f a f a l l i n g o b j e c t
Milliseconds 82 74 236 133 171 59 102 49 102 70 70 179 65 91 145 83 63 76 40 297 118 103 91 203 143
Character c h a n g e a s a f u n c t i o n o f
Milliseconds 95 190 60 113 64 62 53 104 82 91 65 159 107 99 110 170 43 134 30 51 80 36 105 38 87
Character t i m e ? H o w d o e s t h e l e v e l
Milliseconds 92 29 108 15 325 104 238 229 87 124 178 106 87 56 77 87 31 53 71 44 128 91 98 48 125
Character o f w a t e r i n a b a r r e l c h a n
Milliseconds 71 75 81 164 130 37 132 62 75 91 71 70 73 104 169 172 44 178 39 86 77 178 55 87 79
Character g e a s a f u n c t i o n o f t h e a
Milliseconds 54 51 97 161 37 97 203 101 206 98 126 65 122 43 35 62 59 117 22 63 98 34 21 99 144
Character m o u n t o f l i q u i d p o u r e d i n
Milliseconds 137 84 105 165 27 154 44 141 63 31 111 97 128 67 135 26 235 34 92 151 77 188 187 24 60
Character t o i t ? W e s e e c h a n g e o c c u
Milliseconds 69 81 172 0 55 238 160 148 166 89 111 66 161 65 93 58 91 80 63 90 62 184 37 130 119
Character r r i n g i n n e a r l y e v e r y t h i n
Milliseconds 50 152 99 49 68 73 59 65 75 165 82 48 41 92 138 61 153 161 112 48 60 130 89 79 79
Character g w e o b s e r v e i n t h e w o r l d
Milliseconds 62 99 136 55 118 124 34 176 95 92 163 100 75 59 86 77 92 48 48 75 131 41 88 79 71
Character a n d u n -n -u -d - d u n i v e r s e , a n
Milliseconds 76 88 33 120 8 140 176 277 158 141 138 79 83 167 185 68 57 157 82 83 82 55 72 87 48
Character d p o w e r f u l m o d e r n i n s t r u m
Milliseconds 57 38 100 43 84 27 81 84 89 62 83 133 68 46 167 25 105 84 127 45 128 80 212 105 145
Character e n t s h e l p u s s e e m o r e a n d
Milliseconds 89 76 65 81 90 127 70 124 84 59 122 64 94 105 32 182 43 90 43 30 52 47 133 25 113
Character m o r e . -. - . I n t h i s s e c t i o
Milliseconds 90 61 71 90 65 108 171 231 106 177 80 183 159 95 44 122 0 72 69 112 71 194 153 52 50
Character n w e i n t r o d u c e t h e i d e a s
Milliseconds 60 32 80 75 69 140 35 81 155 40 128 119 94 130 100 111 93 21 84 109 44 141 57 95 91
Character o f a v e r a g e a n d i n s t a n t a n e
Milliseconds 97 103 72 117 152 203 58 119 65 56 115 83 22 112 61 96 68 94 72 122 131 191 137 149 235
Character o u s r a t e s o f c h a n g e , a n d
Milliseconds 236 44 186 120 224 106 97 63 53 103 107 66 83 120 50 117 50 91 43 73 57 76 88 32 153
Character s h o w t h a t t h e y a r e c l o s e l
Milliseconds 138 150 55 68 93 104 67 74 41 119 85 39 80 86 53 107 26 41 40 173 44 150 70 21 75
Character y r e l a t e d t o t h e s l o p e o f
Milliseconds 164 47 107 32 98 299 24 61 140 109 44 40 102 74 62 31 96 125 81 151 95 72 124 105 49
Character a s -s c u r v e a t a p o i n t P o
Milliseconds 141 41 128 590 329 76 109 275 196 129 73 150 37 92 83 104 92 42 84 109 0 106 191 186 128
Character n t h e c u r v e . W e g i v e p r e c
Milliseconds 71 100 45 38 45 92 148 472 106 738 135 114 131 258 162 102 94 40 136 25 114 116 50 76 163
Character i s e d e v e l o p m e n t s o f t h e s e
Milliseconds 217 143 56 73 184 159 165 59 92 169 85 140 110 107 37 72 111 54 63 95 95 29 68 92 116
Character i m p o r t a n t c o n c e p t s i n t h
Milliseconds 34 108 94 81 33 83 170 91 108 127 86 260 106 42 99 146 44 108 131 152 105 68 58 78 46
Character e n e x t c h a p t e r , b u t f o r n
Milliseconds 45 83 85 83 169 170 105 188 66 88 78 96 121 78 106 76 179 79 81 50 138 0 194 162 139
Character o w s -s w e u s e a n i n f o r m a l p
Milliseconds 23 51 120 172 328 66 71 46 203 41 72 43 149 39 112 106 62 117 110 106 109 184 76 100 207
Character a p -p -a -p a p p r o a c h s o y o u w i l l
Milliseconds 8 222 303 125 142 115 86 131 144 81 87 160 71 89 157 42 97 160 37 106 44 90 64 63 117
Character s e e h o w t h e y l e a d n a t u r a
Milliseconds 142 588 62 177 121 110 24 60 67 50 64 89 63 59 119 77 83 97 94 137 60 66 373 82 90
Character l l y t o t h e m a i n i d e a o f t
Milliseconds 51 157 87 70 97 36 103 54 66 33 75 106 68 65 86 90 104 85 159 62 63 34 77 101 94
Character h i s c h a p t e r , t h e l i m i t . T
Milliseconds 55 42 43 139 186 90 107 40 121 110 61 113 79 115 41 87 27 135 103 85 118 107 87 101 182
Character h e i d e a o f -f - -o o f a l i m i t
Milliseconds 104 69 82 102 62 167 61 209 38 135 312 146 135 150 61 41 128 42 128 398 163 113 111 134 133
Character p l a y s a f o u n d a t i o n a l r o l e
Milliseconds 159 35 155 80 80 99 113 82 94 73 74 133 28 115 36 36 74 26 76 101 67 293 0 104 79
Character t h r o u g h o u t c l -l a l c u l u s .
Milliseconds 75 95 46 115 72 65 93 83 70 96 74 121 166 134 306 72 100 117 156 45 166 146 90
WPM Timing
Seconds WPM
1.87 32.14
3.73 70.7
5.6 85.7
7.47 101.24
9.33 89.99
11.2 93.2
13.07 99.17
14.94 98.83
16.8 100.7
18.67 102.2
20.54 104.01
22.4 106.06
24.27 107.29
26.14 107.89
28 110.13
29.87 110.88
31.74 110.78
33.6 111.77
35.47 112.31
37.34 112.16
39.21 111.41
41.07 112.48
42.94 113.18
44.81 112.48
46.67 113.64
48.54 114.21
50.41 114.51
52.27 113.63
54.14 114.59
56.01 115.48
57.87 116.11
59.74 113.89
61.61 114.53
63.48 112.48
65.34 112.21
67.21 112.48
69.08 112.74
70.94 112.82
72.81 112.9
74.68 112.64
76.54 111.15
78.41 110.95
80.28 111.36
82.14 111.75
84.01 112.27
85.88 112.48
87.75 111.05
89.61 111.01
91.48 111.76
93.35 111.07