Using matlab code Consider the following function Hs nsds w

Using matlab code:

Consider the following function: H(s) = n(s)/d(s) where: n(s) = s^4 + 6s^3 + 5s^2 + 4s + 3 d(s) = s^5 + 7s^4 + 6s^3 + 5s^2 + 4s + 7 Use MATLAB to find the following: n(-10) d(-5) H(-3) Use MATLAB to find the partial fraction expansions of the following: G(s) = 3s +1/s^2 + 3s + 2; H(s) = (s + 3)(s + 4)/(s^2 + 17s^2 + 79s + 63) Consider the two polynomials: p(s) = s^2 - 7s + 12 and q(s) =s + 2. Using MATLAB, compute the following: p(s) * q(s) p(s)/q(s) (find the quotient and the remainder) Roots of p(s) and q(s) p(5)and q(-3). Partial Fraction expansion of: q(s)/p(s) Also find the Partial Fraction expansion of q(s)/p(s) analytically (by hand), and compare with the result obtained using MATLAB (in part (c)). Use MATLAB to obtain the first and second derivatives of the following functions: F(x) = x^5 - 8x^4 + 5x^3 - 7x^2 + 11x - 9 F(x) = (x^3 + 3x - 8)(x^2 + 21) F(x) = (3x^3 - 8x^2 + 5x + 9)/(x + 2) Consider the following system of linear algebraic equations: x + 2y = 2, 2x + 2y = 6 Obtain the solution to the above system of equations using three different approaches: using Matrix inverse Using Symbolic Math graphically Given the following expressions for p_1 and p_2. P_1 = 5x^2 + 7 p_2 = 5x^2 - 6x + 7 Compute the following: dp_2/dx d(p_1p_2)/dx d(p_2/p_1)/dx

Solution

i : To find n(-10), substitute s=-10 into the function n(s)=s⁴ +6s³ +5s²+4s+3.

So, n(-10)=(-10)⁴ +6(-10)³ +5(-10)²+4(-10)+3

=10000-6000+500-40+3

=4463

ii : To find d(-5), substitute s=-5 into the function d(s)=s⁵ +7s⁴ +6s³+5s²+4s+7

So, d(-5)=(-5)⁵ +7(-5)⁴ +6(-5)³+5(-5)²+4(-5)+7

=-3125+4375-750+125-20+7

=612