Facits til Miniprojekt A - matdat.life.ku.dk
Facits til Miniprojekt A - matdat.life.ku.dk
Facits til Miniprojekt A - matdat.life.ku.dk
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
<strong>Facits</strong> <strong>til</strong> <strong>Miniprojekt</strong> A Matematik og databehandling 2012<br />
Opgave 3 (30%)<br />
(a) f ′ (t) = 2lnt+2 og f ′′ (t) = 2/t fører <strong>til</strong><br />
f 1 (t) = 2(t−1) og f 2 (t) = 2(t−1)+(t−1) 2 .<br />
(b) Graferne for f(t), f 1 (t) og f 2 (t) for 0 ≤ t ≤ 2:<br />
−2 −1 0 1 2 3<br />
f(t)<br />
f 1 (t)<br />
f 2 (t)<br />
0.0 0.5 1.0 1.5 2.0<br />
t<br />
(c) Grafen for |f(t)−f 2 (t)| for 1 ≤ t ≤ 2:<br />
|f(t) − f 2(t)|<br />
0.00 0.05 0.10 0.15 0.20<br />
1.0 1.2 1.4 1.6 1.8 2.0<br />
t<br />
Af nedenstående “forstørrelse” ses det, at |f(t)−f 2 (t)| ≤ 0.04 for 1 ≤ t ≤ 1.53.<br />
|f(t) − f 2(t)|<br />
0.038 0.039 0.040 0.041<br />
1.520 1.525 1.530 1.535 1.540<br />
t<br />
5
Change language