Key (malformant)

Race #8738

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Official speed 87.55 wpm (118.42 seconds elapsed during race)
Without ending ping 87.68 wpm (178 ms delay sending score to TypeRacer’s server)
Timerless 88.13 wpm (597 ms elapsed before first character typed; 117.65 seconds elapsed during race)
Timerless minus one 88.02 wpm, ignoring the first character typed
Race Start August 25, 2023 10:20:08am UTC
Race Finish August 25, 2023 10:22:06am UTC
Outcome Win (1 of 5)
Opponents 2. rajnishkumar31 (79.76 wpm)
3. jvgcalites (79.69 wpm)
5. qw_slow_typist (68.21 wpm)
Accuracy 96.8%
Points 236.39
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 ia s a tool that helps us understand hoqw a change in one qunantity is related to a change in another. How does the speed od f a faillifalling 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 tiit? We see change occrugurring in nearly everything we observe in the world and univseerse, and powerduful modern intstruments help us see more and more. In this sedction we uinintroduce the ideas of avegrerage and instanteaneous rates of change, and show that they are closel y y realted realtedrelated to the slope of a curve at apo point P on the curve. We give precise developments of these important concepts in the next chapter, but for newnow we use an informal approach so you will see how they lead natuerrally ot to the main idea of this chapter, the limit. The idea of a limit players playus a plays a foundatino rfoundational ruole throughout coalculus.
Timing
Character C a l c u l u s i a - -a s a t o o l t h
Milliseconds 597 233 128 104 135 185 191 137 64 87 112 81 385 144 104 80 112 31 184 80 136 160 72 73 103
Character a t h e l p s u s u n d e r s t a n d h o
Milliseconds 80 184 66 78 80 136 72 80 88 97 87 64 96 40 56 145 67 141 189 154 33 126 48 73 55
Character q -q w a c h a n g e i n o n e q u n -n a
Milliseconds 73 504 104 104 144 107 133 72 88 80 80 56 88 56 54 72 139 79 80 80 128 96 224 529 79
Character n t i t y i s r e l a t e d t o a c h a
Milliseconds 96 136 79 105 103 129 120 96 104 128 47 105 81 135 23 145 80 104 55 57 112 72 104 71 81
Character n g e i n a n o t h e r . H o w d o e s
Milliseconds 80 80 23 81 105 87 80 160 81 47 88 96 78 49 97 64 168 72 112 55 121 63 88 145 56
Character t h e s p e e d o d - -d f a f a i l l i
Milliseconds 112 39 137 72 96 112 65 95 168 80 32 104 88 408 144 112 72 116 92 15 129 120 160 137 175
Character -f -a -i -l -l -i f a l l i n g o b j e c t c h a n
Milliseconds 225 0 0 0 0 0 159 96 128 128 120 71 73 76 100 80 88 88 160 176 57 127 64 104 72
Character g e a s a f u n c t i o n o f t i m e ?
Milliseconds 88 40 88 120 81 103 88 63 153 94 42 120 152 40 144 40 88 96 64 64 104 64 54 48 210
Character H o w d o e s t h e l e v e l o f w a
Milliseconds 136 200 135 55 84 118 55 121 144 80 87 74 86 56 73 48 95 81 80 22 162 15 105 127 153
Character t e r i n a b a r r e l c h a n g e a s
Milliseconds 112 110 50 88 128 46 57 145 112 152 144 208 104 176 144 56 144 71 88 89 160 88 119 162 87
Character a f u n c t i o n o f t h e a m o u n t
Milliseconds 80 104 41 151 72 47 81 176 24 184 55 104 105 88 40 127 24 112 65 288 136 150 160 56 98
Character o f l i q u i d p o u r e d i n t o t i
Milliseconds 72 104 78 58 159 171 214 136 192 144 95 239 177 217 144 152 152 168 158 66 120 80 113 159 95
Character -i -t i t ? W e s e e c h a n g e o c c r u
Milliseconds 417 126 186 104 239 137 166 186 64 184 152 111 90 111 64 87 81 64 40 96 256 144 128 208 72
Character g -g -u -r u r r i n g i n n e a r l y e v e r
Milliseconds 272 216 152 136 216 72 111 137 47 65 72 72 56 79 257 128 168 176 55 177 87 393 112 128 46
Character y t h i n g w e o b s e r v e i n t h e
Milliseconds 834 152 72 38 113 64 89 96 96 80 96 152 112 96 80 176 88 54 106 56 40 112 64 87 33
Character w o r l d a n d u n i v s e -e -s e r s e , a
Milliseconds 112 54 106 96 62 66 104 74 78 64 66 52 114 113 151 158 354 143 137 40 152 96 120 80 72
Character n d p o w e r d u -u -d f u l m o d e r n i n
Milliseconds 112 80 54 82 120 96 96 87 209 64 320 136 104 71 143 98 112 70 185 417 136 232 120 103 81
Character t -t s t r u m e n t s h e l p u s s e e m
Milliseconds 143 545 88 127 48 89 136 63 73 112 208 80 128 120 128 80 176 144 96 96 136 152 128 72 103
Character o r e a n d m o r e . I n t h i s s e d
Milliseconds 47 82 15 89 88 80 72 62 74 64 55 24 153 48 168 152 56 120 80 22 106 39 129 144 168
Character -d c t i o n w e u i n -n -i -u i n t r o d u c e
Milliseconds 400 88 168 64 136 48 63 113 89 87 200 0 23 417 144 144 168 46 90 23 97 96 103 104 89
Character t h e i d e a s o f a v e g -g -e r -r e r a
Milliseconds 62 234 72 88 63 201 144 136 168 105 110 105 88 80 168 207 185 184 432 134 89 329 384 176 440
Character g e a n d i n s t a n t e -e a n e o u s r a
Milliseconds 152 72 112 126 82 104 46 90 64 80 304 184 96 126 242 296 129 111 230 354 55 169 64 200 182
Character t e s o f c h a n g e , a n d s h o w t
Milliseconds 130 40 136 56 96 72 64 103 65 88 95 64 56 105 88 120 136 176 72 96 111 48 81 72 143
Character h a t t h e y a r e c l o s e l y - -y -
Milliseconds 97 119 177 79 73 72 94 74 65 71 152 46 65 129 96 144 112 31 106 119 104 176 288 136 136
Character y r e a l t e d -r -e -a -l -t -e -d - r e a l t e d
Milliseconds 224 80 96 39 153 96 103 23 146 112 127 0 0 0 0 0 0 0 233 32 160 54 137 41 152
Character -r -e -a -l -t -e -d r e l a t e d t o t h e s l o
Milliseconds 192 0 0 0 0 0 0 280 54 226 128 144 40 152 62 122 47 47 82 80 71 80 80 104 217
Character p e o f a c u r v e a t a p o -o -p p o
Milliseconds 200 119 57 136 120 71 161 72 168 167 112 169 72 79 137 208 88 160 281 223 232 152 128 96 200
Character i n t P o n t h e c u r v e . W e g i
Milliseconds 168 46 90 63 217 127 265 55 89 112 64 87 47 138 128 119 153 56 150 49 153 176 80 151 129
Character v e p r e c i s e d e v e l o p m e n t s o
Milliseconds 111 96 73 136 97 47 169 119 80 112 89 151 160 121 71 88 160 176 176 65 103 96 192 32 96
Character f t h e s e i m p o r t a n t c o n c e p t
Milliseconds 104 55 105 72 104 144 97 71 144 80 199 40 121 47 146 72 135 80 337 279 88 144 80 160 128
Character s i n t h e n e x t c h a p t e r , b u
Milliseconds 175 89 96 55 25 103 64 97 48 80 72 160 184 56 136 88 88 120 104 104 47 105 80 128 39
Character t f o r n e w -n -e -w n o w w e u s e a n
Milliseconds 105 32 168 80 96 72 168 94 42 344 0 0 328 63 97 105 95 105 95 47 113 80 97 103 88
Character i n f o r m a l a p p r o a c h s o y o u
Milliseconds 88 90 54 80 88 88 57 119 112 72 176 89 135 88 112 81 127 112 15 121 112 23 193 120 56
Character w i l l s e e h o w t h e y l e a d n
Milliseconds 81 87 56 160 136 56 128 152 128 88 120 48 49 79 128 40 112 40 81 175 40 153 71 96 112
Character a t u e r -r -e r a l l y o t -o -t - t o t h e
Milliseconds 80 152 96 88 0 488 360 104 168 80 127 169 72 224 88 184 297 0 0 207 40 88 72 64 96
Character m a i n i d e a o f t h i s c h a p t e
Milliseconds 48 120 80 80 56 62 186 112 128 160 56 55 121 64 120 72 40 136 128 160 70 90 104 96 96
Character r , t h e l i m i t . T h e i d e a o f
Milliseconds 47 106 103 136 96 80 40 96 176 80 80 112 120 88 152 86 90 64 104 73 135 144 104 88 104
Character a l i m i t p l a y e r s -p -l -a -y -e -r -s -
Milliseconds 65 103 80 23 200 97 96 128 64 96 88 62 177 49 63 129 88 272 0 0 0 0 0 0 0
Character p l a y u s a -a - -p -l -a -y -u -s - p l a y s a
Milliseconds 344 96 143 113 24 72 96 104 72 167 0 137 0 0 0 0 0 0 1704 47 137 152 104 104 136
Character f o u n d a t i n o r -r -f -o -u -n -d -a -t -i -n -o -
Milliseconds 71 129 71 162 54 73 144 168 40 160 0 96 176 327 160 0 0 0 0 0 0 0 0 0 0
Character f o u n d a t i o n a l r u -u o l e t h r o u
Milliseconds 361 80 216 72 120 184 184 47 145 55 153 104 88 96 88 272 320 160 80 55 145 96 120 63 177
Character g h o u t c o -o a l c u l u s .
Milliseconds 511 89 184 47 145 80 208 64 488 88 120 89 127 193 151 96 80
WPM Timing
Seconds WPM
2.37 50.67
4.74 78.53
7.11 84.44
9.47 86.13
11.84 95.25
14.21 102.18
16.58 95.54
18.95 95.63
21.32 99.64
23.68 102.34
26.05 102.71
28.42 103.86
30.79 102.5
33.16 99.52
35.53 98.97
37.9 96.58
40.26 94.48
42.63 96.83
45 96.26
47.37 95.5
49.74 94.09
52.11 95.11
54.47 95.16
56.84 94.79
59.21 94.04
61.58 91.59
63.95 90.82
66.32 91.56
68.69 92.77
71.05 90.52
73.42 89.4
75.79 89.77
78.16 88.89
80.53 89.26
82.9 89.61
85.27 90.49
87.63 90.65
90 90.8
92.37 91.46
94.74 92.08
97.11 92.31
99.48 91.32
101.84 92.02
104.21 92.69
106.58 92.1
108.95 90.1
111.32 89.04
113.69 88.35
116.06 87.89
118.42 87.55