Official speed |
74.52 wpm (139.13 seconds elapsed during race) |
Without ending ping |
74.70 wpm (335 ms delay sending score to TypeRacer’s server) |
Timerless |
75.27 wpm (1,055 ms elapsed before first character typed; 137.74 seconds elapsed during race) |
Timerless minus one |
75.19 wpm, ignoring the first character typed |
Race Start |
September 19, 2023 6:58:54pm UTC |
Race Finish |
September 19, 2023 7:01:13pm UTC |
Outcome |
No win (3 of 4) |
Opponents |
1. mahomes_pat (90.97 wpm)
|
Accuracy |
95.9% |
Points |
201.20 |
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 |
Calcuslulusi s a is a tool that helupps us understand how ca ca change in one quantity is related to a change in another. How does the speed of a lafalling object change as a fucntnction of time? How does the level of water in a barrel change as a functino ofon of the amound of t of loiquid poured into it? Wee see change occuriring in nearly everyhingthing we observe in the world and universe, and powerful mofdern instruments hoeelp us see more naand more. Int h this seciction we introduce the ideas of average and instatntaneious rates of change, and whoshow taht hat they are closely related to the slope of a cuve rve at a point P on the cuvrceve. We give precise developments of these important comnceppts in the next chapter, but for now e uew we use an informal approaarchach seo you will see thhow they lead naturally tho tehe main idea of this chapter, the limit. The iedea oa f a limit plays a fuoundational role throughout calculus. |
Timing |
Character |
C |
a |
l |
c |
u |
s |
l |
u |
-u |
-l |
-s |
l |
u |
s |
i |
|
s |
|
a |
|
- |
-a |
- |
-s |
- |
Milliseconds |
1055 |
204 |
94 |
108 |
108 |
110 |
93 |
123 |
279 |
138 |
109 |
234 |
108 |
110 |
123 |
16 |
140 |
46 |
125 |
77 |
201 |
124 |
108 |
125 |
108 |
Character |
-i |
|
i |
s |
|
a |
|
t |
o |
o |
l |
|
t |
h |
a |
t |
|
h |
e |
l |
u |
p |
-p |
-u |
p |
Milliseconds |
108 |
155 |
138 |
94 |
77 |
92 |
77 |
93 |
109 |
111 |
154 |
77 |
123 |
109 |
79 |
29 |
341 |
155 |
93 |
109 |
232 |
109 |
249 |
109 |
216 |
Character |
s |
|
u |
s |
|
u |
n |
d |
e |
r |
s |
t |
a |
n |
d |
|
h |
o |
w |
|
c |
a |
|
c |
-c |
Milliseconds |
78 |
78 |
61 |
96 |
91 |
247 |
157 |
106 |
155 |
63 |
108 |
111 |
61 |
144 |
75 |
93 |
62 |
79 |
92 |
78 |
171 |
32 |
108 |
138 |
202 |
Character |
- |
-a |
-c |
a |
|
c |
h |
a |
n |
g |
e |
|
i |
n |
|
o |
n |
e |
|
q |
u |
a |
n |
t |
i |
Milliseconds |
139 |
116 |
117 |
123 |
77 |
139 |
126 |
93 |
108 |
79 |
95 |
64 |
89 |
78 |
93 |
108 |
140 |
200 |
77 |
387 |
78 |
140 |
358 |
247 |
155 |
Character |
t |
y |
|
i |
s |
|
r |
e |
l |
a |
t |
e |
d |
|
t |
o |
|
a |
|
c |
h |
a |
n |
g |
e |
Milliseconds |
93 |
78 |
46 |
111 |
91 |
62 |
109 |
77 |
202 |
265 |
125 |
77 |
186 |
77 |
157 |
32 |
306 |
139 |
78 |
136 |
110 |
78 |
123 |
76 |
63 |
Character |
|
i |
n |
|
a |
n |
o |
t |
h |
e |
r |
. |
|
H |
o |
w |
|
d |
o |
e |
s |
|
t |
h |
e |
Milliseconds |
63 |
78 |
93 |
109 |
169 |
79 |
108 |
81 |
122 |
92 |
31 |
78 |
124 |
172 |
201 |
141 |
109 |
155 |
139 |
78 |
92 |
33 |
200 |
78 |
93 |
Character |
|
s |
p |
e |
e |
d |
|
o |
f |
|
a |
|
l |
a |
-a |
-l |
f |
a |
l |
l |
i |
n |
g |
|
o |
Milliseconds |
61 |
123 |
47 |
139 |
156 |
156 |
47 |
110 |
107 |
94 |
108 |
64 |
121 |
124 |
201 |
124 |
108 |
31 |
95 |
124 |
142 |
77 |
63 |
48 |
76 |
Character |
b |
j |
e |
c |
t |
|
c |
h |
a |
n |
g |
e |
|
a |
s |
|
a |
|
f |
u |
c |
n |
t |
-t |
-n |
Milliseconds |
110 |
170 |
93 |
172 |
136 |
78 |
154 |
108 |
95 |
92 |
49 |
105 |
31 |
141 |
95 |
93 |
123 |
62 |
326 |
120 |
108 |
187 |
45 |
278 |
139 |
Character |
-c |
n |
c |
t |
i |
o |
n |
|
o |
f |
|
t |
i |
m |
e |
? |
|
H |
o |
w |
|
d |
o |
e |
s |
Milliseconds |
125 |
217 |
93 |
124 |
48 |
94 |
76 |
93 |
108 |
125 |
30 |
172 |
93 |
62 |
77 |
280 |
108 |
188 |
419 |
187 |
108 |
171 |
80 |
95 |
76 |
Character |
|
t |
h |
e |
|
l |
e |
v |
e |
l |
|
o |
f |
|
w |
a |
t |
e |
r |
|
i |
n |
|
a |
|
Milliseconds |
46 |
138 |
62 |
108 |
46 |
94 |
94 |
62 |
92 |
140 |
15 |
562 |
136 |
62 |
174 |
107 |
107 |
125 |
60 |
66 |
120 |
125 |
95 |
108 |
77 |
Character |
b |
a |
r |
r |
e |
l |
|
c |
h |
a |
n |
g |
e |
|
a |
s |
|
a |
|
f |
u |
n |
c |
t |
i |
Milliseconds |
141 |
108 |
140 |
142 |
92 |
125 |
64 |
122 |
111 |
29 |
157 |
44 |
109 |
32 |
140 |
124 |
77 |
109 |
93 |
140 |
123 |
141 |
64 |
137 |
64 |
Character |
n |
o |
|
o |
f |
-f |
-o |
- |
-o |
-n |
o |
n |
|
o |
f |
|
t |
h |
e |
|
a |
m |
o |
u |
n |
Milliseconds |
123 |
0 |
77 |
155 |
93 |
341 |
122 |
108 |
124 |
109 |
311 |
123 |
157 |
138 |
110 |
77 |
139 |
62 |
123 |
32 |
357 |
141 |
109 |
80 |
167 |
Character |
d |
|
o |
f |
|
- |
-f |
-o |
- |
-d |
t |
|
o |
f |
|
l |
o |
-o |
i |
q |
u |
i |
d |
|
p |
Milliseconds |
81 |
59 |
80 |
105 |
62 |
279 |
124 |
124 |
110 |
123 |
185 |
109 |
323 |
108 |
77 |
61 |
203 |
528 |
218 |
111 |
122 |
109 |
264 |
77 |
156 |
Character |
o |
u |
r |
e |
d |
|
i |
n |
t |
o |
|
i |
t |
? |
|
W |
e |
e |
-e |
|
s |
e |
e |
|
c |
Milliseconds |
124 |
216 |
140 |
64 |
215 |
47 |
125 |
63 |
109 |
93 |
107 |
157 |
110 |
252 |
170 |
170 |
251 |
171 |
296 |
139 |
109 |
108 |
123 |
202 |
297 |
Character |
h |
a |
n |
g |
e |
|
o |
c |
c |
u |
r |
i |
-i |
r |
i |
n |
g |
|
i |
n |
|
n |
e |
a |
r |
Milliseconds |
108 |
77 |
126 |
47 |
76 |
61 |
155 |
77 |
158 |
107 |
185 |
76 |
527 |
141 |
76 |
110 |
62 |
63 |
110 |
76 |
92 |
205 |
120 |
249 |
95 |
Character |
l |
y |
|
e |
v |
e |
r |
y |
h |
i |
n |
g |
-g |
-n |
-i |
-h |
t |
h |
i |
n |
g |
|
w |
e |
|
Milliseconds |
216 |
79 |
61 |
123 |
94 |
107 |
109 |
110 |
92 |
78 |
127 |
90 |
250 |
263 |
108 |
94 |
261 |
94 |
95 |
122 |
63 |
30 |
357 |
92 |
155 |
Character |
o |
b |
s |
e |
r |
v |
e |
|
i |
n |
|
t |
h |
e |
|
w |
o |
r |
l |
d |
|
a |
n |
d |
|
Milliseconds |
202 |
201 |
173 |
75 |
327 |
186 |
60 |
94 |
77 |
94 |
109 |
231 |
97 |
75 |
62 |
280 |
108 |
93 |
92 |
93 |
77 |
94 |
95 |
90 |
63 |
Character |
u |
n |
i |
v |
e |
r |
s |
e |
, |
|
a |
n |
d |
|
p |
o |
w |
e |
r |
f |
u |
l |
|
m |
o |
Milliseconds |
123 |
402 |
138 |
78 |
140 |
62 |
124 |
62 |
171 |
77 |
93 |
92 |
94 |
61 |
98 |
72 |
203 |
31 |
66 |
200 |
60 |
125 |
123 |
355 |
109 |
Character |
f |
-f |
d |
e |
r |
n |
|
i |
n |
s |
t |
r |
u |
m |
e |
n |
t |
s |
|
h |
o |
e |
-e |
-o |
e |
Milliseconds |
296 |
263 |
110 |
156 |
46 |
93 |
92 |
124 |
79 |
60 |
92 |
233 |
156 |
172 |
93 |
109 |
61 |
112 |
46 |
94 |
105 |
61 |
346 |
373 |
140 |
Character |
l |
p |
|
u |
s |
|
s |
e |
e |
|
m |
o |
r |
e |
|
n |
a |
-a |
-n |
a |
n |
d |
|
m |
o |
Milliseconds |
107 |
140 |
154 |
110 |
125 |
79 |
295 |
203 |
140 |
78 |
95 |
58 |
62 |
77 |
47 |
172 |
30 |
418 |
138 |
202 |
93 |
108 |
60 |
63 |
78 |
Character |
r |
e |
. |
|
I |
n |
t |
|
h |
-h |
- |
-t |
|
t |
h |
i |
s |
|
s |
e |
c |
i |
-i |
c |
-c |
Milliseconds |
62 |
63 |
245 |
78 |
185 |
202 |
201 |
95 |
201 |
217 |
128 |
105 |
123 |
140 |
32 |
124 |
90 |
217 |
125 |
124 |
201 |
108 |
468 |
326 |
331 |
Character |
t |
i |
o |
n |
|
w |
e |
|
i |
n |
t |
r |
o |
d |
u |
c |
e |
|
t |
h |
e |
|
i |
d |
e |
Milliseconds |
121 |
108 |
94 |
47 |
63 |
156 |
76 |
123 |
154 |
78 |
62 |
170 |
94 |
107 |
109 |
109 |
154 |
78 |
108 |
94 |
76 |
77 |
95 |
153 |
436 |
Character |
a |
s |
|
o |
f |
|
a |
v |
e |
r |
a |
g |
e |
|
a |
n |
d |
|
i |
n |
s |
t |
a |
t |
-t |
Milliseconds |
185 |
126 |
153 |
172 |
77 |
61 |
140 |
124 |
123 |
80 |
124 |
95 |
104 |
63 |
279 |
92 |
78 |
62 |
108 |
108 |
32 |
94 |
79 |
199 |
373 |
Character |
n |
t |
a |
n |
e |
i |
-i |
o |
u |
s |
|
r |
a |
t |
e |
s |
|
o |
f |
|
c |
h |
a |
n |
g |
Milliseconds |
232 |
93 |
139 |
265 |
311 |
217 |
327 |
231 |
108 |
63 |
92 |
328 |
90 |
174 |
91 |
156 |
108 |
79 |
124 |
91 |
152 |
466 |
156 |
109 |
78 |
Character |
e |
, |
|
a |
n |
d |
|
w |
h |
o |
-o |
-h |
-w |
s |
h |
o |
w |
|
t |
a |
h |
t |
|
- |
-t |
Milliseconds |
78 |
248 |
94 |
108 |
110 |
126 |
75 |
169 |
32 |
80 |
401 |
125 |
109 |
154 |
109 |
93 |
17 |
92 |
111 |
170 |
13 |
186 |
93 |
218 |
109 |
Character |
-h |
-a |
h |
a |
t |
|
t |
h |
e |
y |
|
a |
r |
e |
|
c |
l |
o |
s |
e |
l |
y |
|
r |
e |
Milliseconds |
123 |
436 |
218 |
92 |
62 |
78 |
156 |
124 |
126 |
140 |
62 |
155 |
93 |
93 |
61 |
170 |
108 |
171 |
77 |
62 |
156 |
78 |
77 |
124 |
46 |
Character |
l |
a |
t |
e |
d |
|
t |
o |
|
t |
h |
e |
|
s |
l |
o |
p |
e |
|
o |
f |
|
a |
|
c |
Milliseconds |
187 |
109 |
356 |
122 |
201 |
107 |
155 |
30 |
140 |
155 |
124 |
79 |
63 |
139 |
62 |
297 |
204 |
137 |
91 |
94 |
108 |
78 |
77 |
62 |
109 |
Character |
u |
v |
e |
|
- |
-e |
-v |
r |
v |
e |
|
a |
t |
|
a |
|
p |
o |
i |
n |
t |
|
P |
|
o |
Milliseconds |
204 |
120 |
123 |
93 |
309 |
138 |
108 |
607 |
186 |
139 |
91 |
188 |
205 |
94 |
138 |
62 |
187 |
95 |
153 |
139 |
94 |
75 |
155 |
155 |
187 |
Character |
n |
|
t |
h |
e |
|
c |
u |
v |
-v |
r |
c |
e |
-e |
-c |
v |
e |
. |
|
W |
e |
|
g |
i |
v |
Milliseconds |
108 |
79 |
139 |
78 |
76 |
110 |
124 |
202 |
140 |
418 |
126 |
184 |
201 |
280 |
124 |
108 |
78 |
63 |
139 |
279 |
202 |
109 |
327 |
61 |
110 |
Character |
e |
|
p |
r |
e |
c |
i |
s |
e |
|
d |
e |
v |
e |
l |
o |
p |
m |
e |
n |
t |
s |
|
o |
f |
Milliseconds |
111 |
75 |
62 |
108 |
78 |
202 |
92 |
80 |
78 |
108 |
357 |
187 |
124 |
108 |
112 |
199 |
171 |
185 |
125 |
139 |
93 |
125 |
46 |
108 |
109 |
Character |
|
t |
h |
e |
s |
e |
|
i |
m |
p |
o |
r |
t |
a |
n |
t |
|
c |
o |
m |
-m |
n |
c |
e |
p |
Milliseconds |
108 |
109 |
77 |
124 |
108 |
109 |
62 |
124 |
141 |
110 |
140 |
202 |
279 |
93 |
154 |
125 |
77 |
171 |
186 |
171 |
313 |
230 |
63 |
170 |
93 |
Character |
p |
-p |
t |
s |
|
i |
n |
|
t |
h |
e |
|
n |
e |
x |
t |
|
c |
h |
a |
p |
t |
e |
r |
, |
Milliseconds |
156 |
432 |
140 |
92 |
110 |
30 |
93 |
93 |
95 |
122 |
77 |
61 |
93 |
79 |
167 |
61 |
77 |
153 |
94 |
107 |
94 |
170 |
110 |
125 |
61 |
Character |
|
b |
u |
t |
|
f |
o |
r |
|
n |
o |
w |
|
e |
|
u |
-u |
- |
-e |
e |
w |
|
- |
-w |
-e |
Milliseconds |
123 |
142 |
76 |
110 |
77 |
139 |
93 |
107 |
81 |
94 |
75 |
110 |
45 |
156 |
93 |
249 |
219 |
123 |
219 |
215 |
32 |
77 |
268 |
138 |
125 |
Character |
w |
e |
|
u |
s |
e |
|
a |
n |
|
i |
n |
f |
o |
r |
m |
a |
l |
|
a |
p |
p |
r |
o |
a |
Milliseconds |
201 |
15 |
96 |
152 |
123 |
48 |
229 |
189 |
108 |
138 |
108 |
108 |
250 |
91 |
125 |
63 |
123 |
156 |
95 |
111 |
106 |
127 |
107 |
109 |
219 |
Character |
-a |
a |
r |
-r |
-a |
c |
h |
-h |
-c |
a |
c |
h |
|
s |
e |
-e |
o |
|
y |
o |
u |
|
w |
i |
l |
Milliseconds |
281 |
727 |
124 |
310 |
155 |
122 |
142 |
264 |
126 |
156 |
340 |
124 |
78 |
188 |
231 |
234 |
202 |
91 |
92 |
62 |
76 |
48 |
170 |
94 |
154 |
Character |
l |
|
s |
e |
e |
|
t |
h |
-h |
-t |
h |
o |
w |
|
t |
h |
e |
y |
|
l |
e |
a |
d |
|
n |
Milliseconds |
125 |
77 |
125 |
64 |
138 |
109 |
278 |
93 |
218 |
108 |
203 |
63 |
61 |
79 |
123 |
110 |
77 |
109 |
15 |
109 |
107 |
77 |
140 |
50 |
292 |
Character |
a |
t |
u |
r |
a |
l |
l |
y |
|
t |
h |
-h |
o |
|
t |
e |
-e |
h |
e |
|
m |
a |
i |
n |
|
Milliseconds |
112 |
540 |
78 |
233 |
92 |
109 |
155 |
107 |
141 |
360 |
93 |
280 |
246 |
95 |
92 |
188 |
293 |
217 |
77 |
62 |
95 |
124 |
78 |
78 |
78 |
Character |
i |
d |
e |
a |
|
o |
f |
|
t |
h |
i |
s |
|
c |
h |
a |
p |
t |
e |
r |
, |
|
t |
h |
e |
Milliseconds |
156 |
137 |
172 |
62 |
95 |
107 |
78 |
79 |
139 |
61 |
64 |
171 |
46 |
155 |
218 |
97 |
153 |
123 |
326 |
66 |
137 |
96 |
249 |
107 |
110 |
Character |
|
l |
i |
m |
i |
t |
. |
|
T |
h |
e |
|
i |
e |
-e |
d |
e |
a |
|
o |
a |
|
- |
-a |
f |
Milliseconds |
47 |
64 |
120 |
109 |
576 |
203 |
95 |
137 |
418 |
248 |
31 |
95 |
108 |
92 |
326 |
95 |
154 |
79 |
91 |
63 |
311 |
93 |
372 |
140 |
106 |
Character |
|
a |
|
l |
i |
m |
i |
t |
|
p |
l |
a |
y |
s |
|
a |
|
f |
u |
-u |
o |
u |
n |
d |
a |
Milliseconds |
32 |
77 |
108 |
79 |
95 |
169 |
108 |
94 |
62 |
109 |
140 |
124 |
154 |
78 |
91 |
248 |
79 |
231 |
77 |
561 |
234 |
651 |
202 |
154 |
171 |
Character |
t |
i |
o |
n |
a |
l |
|
r |
o |
l |
e |
|
t |
h |
r |
o |
u |
g |
h |
o |
u |
t |
|
c |
a |
Milliseconds |
138 |
78 |
93 |
125 |
170 |
92 |
110 |
77 |
92 |
157 |
63 |
61 |
142 |
90 |
109 |
93 |
109 |
172 |
281 |
136 |
95 |
110 |
80 |
185 |
126 |
Character |
l |
c |
u |
l |
u |
s |
. |
Milliseconds |
60 |
296 |
139 |
155 |
125 |
125 |
79 |
|
WPM Timing |
Seconds |
WPM |
2.78 |
30.19 |
5.57 |
43.13 |
8.35 |
51.75 |
11.13 |
59.3 |
13.91 |
65.55 |
16.7 |
71.16 |
19.48 |
76.39 |
22.26 |
78.7 |
25.04 |
77.63 |
27.83 |
78.92 |
30.61 |
81.55 |
33.39 |
84.45 |
36.17 |
81.27 |
38.96 |
78.86 |
41.74 |
78.2 |
44.52 |
77.09 |
47.3 |
77.88 |
50.09 |
76.67 |
52.87 |
77.17 |
55.65 |
78.27 |
58.43 |
78.65 |
61.22 |
78.21 |
64 |
78.38 |
66.78 |
77.45 |
69.57 |
76.76 |
72.35 |
77.46 |
75.13 |
77.31 |
77.91 |
76.7 |
80.7 |
76.58 |
83.48 |
75.76 |
86.26 |
76.37 |
89.04 |
76.01 |
91.83 |
75.93 |
94.61 |
75.34 |
97.39 |
75.53 |
100.17 |
76.31 |
102.96 |
75.64 |
105.74 |
76.6 |
108.52 |
75.75 |
111.3 |
76.12 |
114.09 |
74.57 |
116.87 |
74.65 |
119.65 |
74.72 |
122.43 |
74.19 |
125.22 |
74.85 |
128 |
74.81 |
130.78 |
74.32 |
133.57 |
74.3 |
136.35 |
74.46 |
139.13 |
74.52 |
|