1. For the sequence
n > 1
compute a real number p such that
lim an = 5
2. Consider the power series
(a) Determine the radius of convergence.
(b) Determine the interval of convergence.
2 e () d.c exactly, we will approximate it using
3. Since it is difficult to evaluate the integral
(a) Determine P3(x), the cubic Maclaurin polynomial of the integrand e (%) .
(b) Obtain an upper bound on the error in the integrand for x in the range
0 < x < L, when the integrand is approximated by P3 (x).
(c) Find an approximation to the original integral by integrating P3 (x).
(d) Obtain an upper bound on the error in the integration in (c).
(e) Use MATLAB to verify your calculation in (a). .
4. Consider the periodic function
- 1 < t < -1
COS (\u ( t + 1))
COS (t), ,
0 < t < 1
with f (t) = f(t+2).
(a) Determine a general expression for the Fourier series of f.
(b) Use MATLAB to plot both f and the sum of the first 5 non-zero terms of the Fourier series
for f on the same set of axes for - 1 < t < 3.
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