Question

7) Use Matlab to compute the following infinite sums ? n=1 7) Find the minima and maxima of the following function f(x) = 1 + x² + 3 sin?(x) – 5 cos? (x) Then plot the function f(x) using MATLAB and verify your results.

Can someone please help me out with this as soon as possible

Answer 1

7) We evaluate the given infinite sums using the syntex
symsum f, n, a, b)
which returns the sum of the series with respect to the summation index (symbolic variable) from the lower bound to the upper bound .

e.g., to evaluate the series $\sum_{n=1}^{4}n^2$ we use the syntex .

symsum(n?, n, 1, 4)

Here, to evaluate the infinite series $\sum_{n=1}^{\infty}\dfrac{3}{n}$ we use the syntex
symsum(3/n, n, 1, Inf)
and when we compile it, we get $\infty$ as out put. (see the following figure)

clc; $clear screen symsn Fl = symsum (3/n,n,1, Inf) Command Window New to MATLAB? See resources for Getting Started. F1 = Inf fx >>

To evaluate the infinite series
انت اية
we use the syntex
symsum(3/n^3, n. 1, Inf)
and when we compile it, we get
3+ 3)=3.6062 ( 3) ~ 1.2021)
as out put. (see the following figure)

clc; $clear screen syms n F2 = symsum (3/n^3, n, 1, Inf) 3- Command Window New to MATLAB? See resources for Getting Started. F2 = 3*zeta (3) fx >>

To evaluate the infinite series $\sum_{n=1}^{\infty}\dfrac{3}{n^4}$ we use the syntex
symsum (3/n 4, n. 1, Inf)
and when we compile it, we get
= 3.2470 (:- *~ 3.1416) 30
as out put. (see the following figure)

clc; $clear screen syms n F3 = symsum (3/n 4,n,1,Inf) Command Window New to MATLAB? See resources for Getting Started. F3 = pi^4/30 fx >>