zak (zak389)

Race #6112

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Official speed 113.09 wpm (91.68 seconds elapsed during race)
Without ending ping 113.55 wpm (373 ms delay sending score to TypeRacer’s server)
Timerless 113.67 wpm (93 ms elapsed before first character typed; 91.21 seconds elapsed during race)
Timerless minus one 113.54 wpm, ignoring the first character typed
Race Start December 30, 2023 11:21:44pm UTC
Race Finish December 30, 2023 11:23:16pm UTC
Outcome No win (11 of 13)
Opponents 1. mth_quitless (159.03 wpm)
2. pastashapes (158.90 wpm)
3. syrupsandwich (155.91 wpm)
4. ginoo75 (152.93 wpm)
5. pokenonquit (152.27 wpm)
6. primalknight (151.15 wpm)
7. keegant (149.00 wpm)
8. hospitalforsouls2 (137.24 wpm)
9. charlieog (135.98 wpm)
10. jlachney (121.19 wpm)
12. jepslol (112.64 wpm)
Accuracy 96.8%
Points 305.34
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 took that tool that helps us understand how a changef in one quantity is related to a chancge in another. How does the speed of a falling object change as a cunfunction of time? How does the level of water in a barrel change as a function of the momeaamount of liquid purououred into iT? t? WE see 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 onintroduce the ideas of average and instantaneous traetetes of change, anod d show that they are closely realyelated to the slope of a vurcurve at a point P on the curve. We give precise developments of these important oconcepts in the next hchpatapter, but for now sew ue use an infrormal aprproach so you will see how they lead naturally to the main idea of this cahpphathpatapter, the limit. THe idhe idea of a limit plays a foundational role throughout claalculus.
Timing
Character C a l c u l u s i s a t o o k t h a t -t
Milliseconds 93 94 46 174 120 266 125 108 47 62 125 78 124 63 62 79 109 61 32 48 75 32 62 48 229
Character -h -a -t - -t -o -o -k - t o o l t h a t h e l p s
Milliseconds 0 0 0 0 109 0 0 0 0 437 77 111 139 47 78 78 50 77 48 78 92 78 32 124 19
Character u s u n d e r s t a n d h o w a c h a n g
Milliseconds 74 93 46 92 125 47 124 47 110 64 31 78 110 48 139 47 62 46 78 92 78 109 30 125 78
Character e f - -f i n o n e q u a n t i t y i s
Milliseconds 30 14 63 218 123 141 377 15 110 91 47 48 45 110 65 94 77 345 33 92 63 76 107 63 33
Character r e l a t e d t o a c h a n c -c g e i n
Milliseconds 169 62 109 92 15 47 155 17 62 93 64 93 95 110 48 126 140 94 372 79 62 16 78 46 78
Character a n o t h e r . H o w d o e s t h e s p e
Milliseconds 32 77 46 33 91 32 47 78 93 156 77 94 79 94 47 94 78 16 110 16 283 79 95 80 79
Character e d o f a f a l l i n g o b j e c t c h
Milliseconds 127 125 48 63 80 48 47 127 15 80 312 111 79 14 47 59 97 125 140 32 46 140 63 299 78
Character a n g e a s a c u n -c -u -n f u n c t i o n
Milliseconds 79 64 78 47 78 110 31 78 94 48 171 78 139 187 0 0 93 93 111 46 142 61 16 33 77
Character o f t i m e ? H o w d o e s t h e l e v
Milliseconds 95 77 32 78 63 30 80 141 125 111 137 47 77 94 63 94 64 13 64 77 77 78 78 62 111
Character e l o f w a t e r i n a b a r r e l c
Milliseconds 46 142 47 141 80 32 93 62 47 109 63 47 95 32 77 31 125 15 94 94 124 32 155 108 94
Character h a n g e a s a f u n c t i o n o f t h
Milliseconds 92 111 111 63 47 62 95 47 92 79 62 95 78 125 46 125 47 16 47 94 76 110 16 124 32
Character e m o m e -e a -m -o -m -a a m o u n t o f l i q
Milliseconds 123 32 78 108 49 94 156 234 187 0 0 0 215 80 47 78 173 78 92 64 79 62 93 47 251
Character u i d p u r o u -u -o -r -u o u r e d i n t o i
Milliseconds 80 48 93 77 295 46 108 61 48 233 140 125 124 202 32 110 64 155 78 15 31 124 32 141 125
Character T ? - -? -T t ? W E s e -e -s - -E e s e e c
Milliseconds 124 124 109 189 125 124 15 205 174 79 357 95 107 62 141 125 124 108 31 63 108 46 111 63 186
Character h a n g e o c c u r r i n g i n n e a r l y
Milliseconds 94 94 31 47 47 47 78 109 126 78 96 126 117 23 78 31 78 32 93 123 63 62 33 139 95
Character e v e r y t h i n g w e o b s e r v e i n
Milliseconds 61 156 79 94 63 64 93 49 46 79 16 62 95 46 77 219 125 92 31 32 185 63 79 109 15
Character t h e w o r l d a n d u n i v e r s e ,
Milliseconds 62 32 61 31 79 79 79 15 238 95 94 93 63 103 22 111 125 31 48 79 93 79 79 111 109
Character a n d p o w e r f u l m o d e r n i n s t r
Milliseconds 79 63 92 32 142 16 94 32 32 142 63 62 94 220 63 62 125 47 64 110 205 77 31 80 47
Character u m e n t s h e l p u s s e e m o r e a
Milliseconds 77 127 78 77 64 63 31 112 110 32 47 95 47 105 34 140 31 173 109 108 48 46 48 48 62
Character n d m o r e . I n t h i s s e c t i o n
Milliseconds 63 77 32 62 48 31 62 78 79 122 78 109 31 47 47 46 62 125 78 77 139 64 31 46 63
Character w e o n -n -o i n t r o d u c e t h e i d e a
Milliseconds 63 46 77 206 122 203 139 236 15 64 30 78 172 79 107 46 62 95 62 93 77 110 78 107 79
Character s o f a v e r a g e a n d i n s t a n t a
Milliseconds 93 95 63 110 46 172 93 109 124 31 125 63 79 78 79 91 46 109 93 48 79 219 109 95 281
Character n e o u s t -t r a e t e -e -t -e t e s o f c h
Milliseconds 125 313 93 46 94 61 96 216 78 46 17 78 79 235 112 109 110 0 46 15 80 79 30 171 109
Character a n g e , a n o d - -d -o d s h o w t h a t
Milliseconds 0 155 64 46 92 95 45 48 62 62 31 343 123 110 359 63 125 93 16 94 62 31 62 47 62
Character t h e y a r e c l o s e l y r e a l y e -e
Milliseconds 62 78 78 108 16 63 123 358 16 93 139 173 125 14 64 93 33 90 93 47 80 14 126 31 253
Character -y -l -a l a t e d t o t h e s l o p e o f
Milliseconds 94 142 108 171 31 32 30 280 125 63 79 78 33 46 92 62 156 47 186 76 187 48 110 80 46
Character a v u r -r -u -v c u r v e a t a p o i n t
Milliseconds 47 93 62 95 79 218 142 111 78 92 93 171 31 47 140 47 32 108 62 127 16 15 32 49 77
Character P o n t h e c u r v e . W e g i v e p
Milliseconds 189 142 108 48 78 30 63 80 48 126 62 78 201 47 93 96 141 64 75 141 62 126 47 48 141
Character r e c i s e d e v e l o p m e n t s o f t h
Milliseconds 16 78 107 96 124 64 64 217 154 78 78 79 124 0 156 32 123 17 95 48 93 77 62 186 47
Character e s e i m p o r t a n t o -o c o n c e p t s
Milliseconds 95 48 125 32 92 48 93 16 46 125 61 47 94 45 233 249 79 95 14 107 48 63 95 93 32
Character i n t h e n e x t h -h c h p a t -t -a -p a p t
Milliseconds 127 30 49 61 47 93 61 46 94 109 64 79 205 237 63 110 80 111 125 139 171 94 92 63 58
Character e r , b u t f o r n o w s e -e -s w u -u -
Milliseconds 113 63 63 109 80 109 46 47 252 64 92 47 32 48 94 30 155 64 206 92 16 95 157 234 95
Character e u s e a n i n f r -r o r m a l a p r -r p
Milliseconds 38 55 81 93 63 64 190 80 93 110 63 95 141 300 184 77 61 94 61 93 158 171 124 375 157
Character r o a c h s o y o u w i l l s e e h o w
Milliseconds 31 188 503 127 95 109 139 94 78 33 62 30 76 47 48 93 110 63 47 62 109 77 48 31 47
Character t h e y l e a d n a t u r a l l y t o t
Milliseconds 48 78 15 312 47 124 31 61 45 111 48 141 80 124 48 343 140 140 110 32 45 94 94 108 110
Character h e m a i n i d e a o f t h i s c a h p
Milliseconds 31 79 61 48 94 30 46 79 140 46 109 62 64 47 110 46 78 31 16 108 47 205 91 78 93
Character -p -h -a p h a t -t -a -h -p h p a t -t -a -p a p t e r ,
Milliseconds 313 140 124 187 16 94 64 267 156 110 126 157 78 109 80 221 126 124 77 112 79 108 47 63 95
Character t h e l i m i t . T H e i d -d -i - -e -H h e
Milliseconds 31 47 64 32 63 48 171 63 80 124 108 79 47 79 47 94 76 125 125 126 109 111 141 63 63
Character i d e a o f a l i m i t p l a y s a f
Milliseconds 47 48 124 31 110 46 142 93 48 110 123 46 141 60 80 31 79 77 110 93 92 30 79 62 62
Character o u n d a t i o n a l r o l e t h r o u g h o
Milliseconds 108 17 124 16 77 65 125 16 15 267 110 156 79 79 141 46 64 110 31 110 16 31 94 48 93
Character u t c l a -a -l a l c u l u s .
Milliseconds 48 47 94 156 112 30 312 76 80 122 80 77 110 126 170 80
WPM Timing
Seconds WPM
1.83 91.62
3.67 78.53
5.5 106.89
7.33 104.71
9.17 109.95
11 112.35
12.84 115.93
14.67 118.62
16.5 115.62
18.34 118.46
20.17 122.56
22 124.89
23.84 123.34
25.67 122.01
27.5 116.93
29.34 114.12
31.17 110.49
33 113.08
34.84 114.7
36.67 116.82
38.51 118.11
40.34 119.59
42.17 121.79
44.01 121.07
45.84 121.47
47.67 121.33
49.51 118.77
51.34 118.5
53.17 118.48
55.01 117.37
56.84 117.17
58.67 116.37
60.51 117.41
62.34 117.8
64.18 118.55
66.01 118.89
67.84 117.8
69.68 117.97
71.51 116.63
73.34 115.51
75.18 114.77
77.01 115.78
78.84 115.82
80.68 115.87
82.51 113.44
84.34 113.53
86.18 112.65
88.01 113.58
89.85 114.2
91.68 113.09