Sequences and series

 

1. Consider the series
X8
n=1
cos(pnp)
v
n + 4
, p ? Z.
Determine the values of p such that the series converges. Justify your answer.
2. Consider the integral
Z 1
2
0
cosh(x
2
) dx.
Since we cannot evaluate the integral exactly, we will approximate it using Maclaurin polynomials.
(a) Determine P4(x), the 4th degree Maclaurin polynomial of the integrand cosh(x
2
).
(b) Use MATLAB to check your answer to part (a).
(c) Find an approximation to the integral by integrating P4(x).
(d) Obtain an upper bound on the magnitude of the error in the integration in part (c).
3. Consider a signal represented by the function
f(t) = t
3
, -1 < t < 1
with f(t) = f(t + 2).
(a) Determine a general Fourier series representation for f.
(b) Use MATLAB to plot both f(t) and the sum of the first 5 non-zero terms of the Fourier
series of f(t) on the same set of axes for -3 = t = 3.

 

find the cost of your paper