qazaqyanke (qazaqyanke)

Race #4783

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Official speed 92.00 wpm (112.70 seconds elapsed during race)
Without ending ping 92.17 wpm (207 ms delay sending score to TypeRacer’s server)
Timerless 92.26 wpm (105 ms elapsed before first character typed; 112.38 seconds elapsed during race)
Timerless minus one 92.15 wpm, ignoring the first character typed
Race Start March 23, 2024 7:03:48am UTC
Race Finish March 23, 2024 7:05:40am UTC
Outcome Win (1 of 2)
Accuracy 98.4%
Points 248.39
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 how a change in one quantity is realtlated to a change in another. How does the speed of a falling object change as a ufunction 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 iuniverse, and powerful modern instruments help us see more and more. TIIn this section we introduce the ideas of eaverage and instantaneous raters os o ff change, and show that they are closely related otto the slope of a uccurve at a point P on the curve. We give precise addevelopments of thes ie important concepts in the next chapter, but for now wsee use ian ifnformal 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.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 105 407 169 96 176 96 144 160 136 8 176 97 119 168 80 88 135 169 57 102 73 120 56 81 103
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 88 119 145 87 64 73 144 80 88 168 72 169 159 48 112 81 151 39 105 127 121 96 96 72 152
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 120 47 137 48 111 153 79 33 130 102 97 95 97 79 216 66 141 74 111 106 110 128 104 104 184
Character r e a l t -t -l -a l a t e d t o a c h a n g
Milliseconds 137 143 152 121 96 151 232 137 151 184 81 63 89 151 96 104 82 86 184 129 151 120 103 73 121
Character e i n a n o t h e r . H o w d o e s t h
Milliseconds 135 71 73 96 95 73 74 78 64 80 112 128 104 112 176 136 112 152 104 96 132 91 73 112 120
Character e s p e e d o f a f a l l i n g o b j e
Milliseconds 71 97 96 88 112 144 152 64 63 136 73 137 135 208 120 104 184 112 96 26 102 73 143 192 88
Character c t c h a n g e a s a u -u f u n c t i o n
Milliseconds 105 199 87 177 72 128 50 101 161 88 95 90 103 112 136 152 464 65 119 184 55 201 74 70 71
Character o f t i m e ? H o w d o e s t h e l e
Milliseconds 58 159 112 104 96 48 98 94 208 175 106 360 111 71 145 88 127 98 70 145 56 136 96 32 112
Character v e l o f w a t e r i n a b a r r e l
Milliseconds 160 136 152 73 200 103 144 40 97 126 89 497 104 118 98 103 113 127 112 112 88 168 161 126 25
Character c h a n g e a s a f u n c t i o n o f t
Milliseconds 416 72 120 87 73 128 120 112 64 168 112 177 175 136 176 80 233 49 62 127 105 128 88 112 113
Character h e a m o u n t o f l i q u i d p o u r e
Milliseconds 103 64 88 105 78 97 128 185 103 55 105 138 70 135 73 208 23 121 122 118 135 402 103 112 161
Character d i n t o i t ? W e s e e c h a n g e
Milliseconds 142 104 121 64 104 88 88 105 62 256 144 241 232 82 110 152 200 79 113 113 120 127 80 192 120
Character o c c u r r i n g i n n e a r l y e v e r y
Milliseconds 344 136 153 23 216 152 111 153 96 96 56 96 104 152 80 112 113 127 120 128 95 168 152 129 112
Character t h i n g w e o b s e r v e i n t h e w
Milliseconds 137 71 136 112 88 160 80 80 127 241 112 64 80 152 135 209 112 72 127 137 128 136 74 78 105
Character o r l d a n d i -i u n i v e r s e , a n d
Milliseconds 103 88 135 81 104 96 161 71 104 96 362 167 206 121 48 192 120 160 137 119 97 103 208 32 119
Character p o w e r f u l m o d e r n i n s t r u m e n
Milliseconds 337 80 112 72 144 120 80 72 159 337 96 8 153 135 120 98 125 137 223 137 96 136 144 129 95
Character t s h e l p u s s e e m o r e a n d m
Milliseconds 127 136 104 88 128 88 160 152 96 152 114 110 104 168 104 104 96 65 152 96 144 111 81 56 57
Character o r e . T I -I -T I n t h i s s e c t i o n
Milliseconds 103 97 119 127 129 176 152 272 128 264 161 143 152 104 80 88 80 144 113 175 248 48 24 167 89
Character w e i n t r o d u c e t h e i d e a s o f
Milliseconds 135 89 152 192 88 80 103 33 192 48 207 131 135 142 81 137 55 128 73 150 97 127 105 171 85
Character e -e a v e r a g e a n d i n s t a n t a n e
Milliseconds 103 129 328 105 95 192 145 202 77 216 79 97 120 88 64 136 128 24 80 120 72 383 353 103 114
Character o u s r a t e r s o -o - -s -r s o f -f - f
Milliseconds 135 104 105 135 240 128 97 119 105 23 72 120 328 160 144 152 112 103 129 249 15 456 136 112 88
Character c h a n g e , a n d s h o w t h a t t h e
Milliseconds 162 102 97 94 64 161 136 113 71 167 41 95 120 129 96 120 88 135 65 127 97 88 96 98 126
Character y a r e c l o s e l y r e l a t e d o t -t
Milliseconds 152 47 80 121 160 81 160 111 136 80 80 136 145 63 128 152 104 105 95 96 168 48 168 104 353
Character -o t o t h e s l o p e o f a u c -c -u c u
Milliseconds 127 89 110 104 90 143 72 73 95 361 231 168 192 80 88 152 80 104 159 169 144 224 120 104 105
Character r v e a t a p o i n t P o n t h e c
Milliseconds 120 135 192 104 98 142 80 120 136 112 63 98 63 88 82 190 168 192 144 48 128 160 80 74 166
Character u r v e . W e g i v e p r e c i s e a d -d
Milliseconds 121 335 135 200 98 128 328 256 127 106 79 175 231 73 136 121 368 392 95 146 134 119 161 120 216
Character -a d e v e l o p m e n t s o f t h e s i -i -
Milliseconds 136 73 159 120 167 489 232 128 184 96 119 82 135 97 143 104 95 137 72 104 128 217 47 425 145
Character e i m p o r t a n t c o n c e p t s i n t
Milliseconds 78 80 96 96 167 66 110 73 112 64 120 127 218 56 138 166 118 106 127 127 122 95 96 104 104
Character h e n e x t c h a p t e r , b u t f o r
Milliseconds 88 113 54 57 89 167 160 80 504 57 103 137 63 113 167 104 105 134 177 72 96 103 128 81 81
Character n o w w s e -e -s e u s e i -i a n i f -f n f
Milliseconds 87 129 111 80 152 10 112 294 168 136 79 161 144 89 87 152 272 89 127 96 112 184 480 184 128
Character o r m a l a p p r o a c h s o y o u w i l
Milliseconds 105 135 81 126 106 136 95 137 158 105 88 112 121 78 138 111 40 152 72 87 113 104 80 48 88
Character l s e e h o w t h e y l e a d n a t u r
Milliseconds 122 94 105 95 144 177 96 127 87 112 177 104 112 80 64 128 105 103 89 95 306 142 64 136 40
Character a l l y t o t h e m a i n i d e a o f
Milliseconds 136 120 136 112 55 128 130 79 104 137 96 71 120 120 104 128 104 112 88 153 127 64 146 69 113
Character t h i s c h a p t e r , t h e l i m i t .
Milliseconds 111 80 104 48 64 272 112 88 144 88 88 152 81 111 138 111 120 39 81 79 80 112 121 128 104
Character T h e i d e a o f a l i m i t p l a y s
Milliseconds 168 136 73 79 95 72 176 104 64 129 103 104 96 153 127 105 105 94 80 98 127 57 95 121 135
Character a f o u n d a t i o n a l r o l e t h r o
Milliseconds 103 88 169 72 82 78 144 72 64 112 80 50 118 49 119 64 136 73 167 112 72 136 48 192 98
Character u g h o u t c a l c u l u s .
Milliseconds 102 135 80 129 127 122 88 151 95 33 169 39 103 105 112 128
WPM Timing
Seconds WPM
2.25 85.19
4.51 98.5
6.76 106.48
9.02 103.82
11.27 95.83
13.52 99.38
15.78 101.16
18.03 101.16
20.29 99.38
22.54 99.03
24.79 98.25
27.05 98.05
29.3 97.88
31.55 98.88
33.81 98.32
36.06 97.16
38.32 97.4
40.57 97.61
42.82 97.79
45.08 96.37
47.33 96.34
49.59 96.32
51.84 96.99
54.09 95.39
56.35 95.41
58.6 95.01
60.86 94.85
63.11 93.55
65.36 92.16
67.62 92.64
69.87 93.09
72.13 92.17
74.38 91.32
76.63 91.76
78.89 91.27
81.14 90.36
83.39 89.5
85.65 88.97
87.9 89.42
90.16 89.58
92.41 89.34
94.66 88.48
96.92 88.9
99.17 89.42
101.43 89.8
103.68 90.16
105.93 90.62
108.19 91.17
110.44 91.81
112.7 92