s(t)=t2
120
dt t s(t) s(t+dt) (s(t+dt)-s(t))/dt
0.0001 0 0 0.00000001 0.0001 100
1 1 1 1.00020001 2.0001
2 4 4.00040001 4.0001 80
Distance
3 9 9.00060001 6.0001
60
4 16 16.00080001 8.0001
5 25 25.00100001 10.0001 40
6 36 36.00120001 12.0001
7 49 49.00140001 14.0001 20
8 64 64.00160001 16.0001
9 81 81.00180001 18.0001 0
0
10 100 100.002 20.0001
3
s(t)=t 1200
dt t s(t) s(t+dt) (s(t+dt)-s(t))/dt
0.0001 0 0 1E-12 0.00000001 1000
1 1 1 1.00030003 3.00030001
2 8 8.00120006 12.00060001 800
Distance
3 27 27.00270009 27.00090001
600
4 64 64.00480012 48.00120001
5 125 125.0075002 75.00150001 400
6 216 216.0108002 108.0018
7 343 343.0147002 147.0021 200
8 512 512.0192002 192.0024
0
9 729 729.0243003 243.0027
0
10 1000 1000.03 300.003
s(t)=exp(t)
dt t s(t) s(t+dt) (s(t+dt)-s(t))/dt 25000
0.0001 0 1 1.000100005 1.000050002
1 1 2.71828 2.71855367 2.718417747 20000
2 7.38906 7.389795041 7.389425564
3 20.0855 20.08754558 20.08654123 15000
Distance
4 54.5982 54.60361012 54.60088003
5 148.413 148.4280012 148.42058 10000
6 403.429 403.4691384 403.4489656
7 1096.63 1096.742827 1096.687992 5000
8 2980.96 2981.256098 2981.10704
9 8103.08 8103.894276 8103.489095 0
0
10 22026.5 22028.66855 22027.56715
s(t)=t2 (s(t+dt)-s(t))/dt
2 4 6 8 10 12
Time
s(t)=t3 (s(t+dt)-s(t))/dt
0 2 4 6 8 10 12
Time
s(t)=exp(t) (s(t+dt)-s(t))/dt
25000
20000
15000
10000
5000
0
0 2 4 6 8 10 12
Time