Which of the following represents the correct taylor

5. Which of the following represents the correct Taylor series expansion for 𝑓𝑓
𝑖𝑖−3
using 𝑥𝑥 = 𝑥𝑥
𝑖𝑖
as the reference
point?
AMME2000/AMME2960 2018
Quiz Solutions, Page 3 of 6

6 . The voltage in a uniform conductor is governed by the differential equation:
V
t
=
1
RC
V
xx
(1)
where V is the voltage, R = 10000 Ω is the resistance and C = 3 × 10
- 3
F is the capacitance. In a 1 m
long conductor, the voltage at both ends of the conductor is regulated to be a constant of 0 V and the
initial voltage distribution takes the form shown in Figure 1.
0 0.2 0.4 0.6 0.8 1
0
2
4
6
8
10
Figure 1: Initial voltage distribution.
(a) [2] Clearly state mathematically the boundary conditions and initial condition of the problem.
(b) [6] Using separation of variables, derive the exact solution to this problem, clearly stating the values
of any parameters in the Fourier Series coefficients.
AMME2000/AMME2960 2018
Quiz Solutions, Page 4 of 6

AMME2000/AMME2960 2018