1. Use Newtons method to find, to 8 significant figures, the positive roots of the following equations:

10e^(sin(x))=(x^2)-5x+4

. Use a tolerance of 10^-8. Use Matlab to solve this problem. (Hint: plotting the function will give you estimates to initialize Newtons method. There are three roots. Find all three.)

2. Modify your code from #1 to solve the following problem. A satellite has a semi-major axis of 15311 km and eccentricity of 0.373. Find the true anomaly of the satellite three hours after it passed perigee.

SOLVE FOR NUMBER 2.

The program is given as clear all xl-input('n Enter value of initial guess') acc input('n Enter value of accuracy finlinex x)-(5*x)+4-(10 exp(sin(x))): df inline(2 x)-5-(10 cos(x)*exp(sin(x)))) ddf inline(2-(10 exp(sin(x)*((cos(x)"cos(x))-sin(x))) yl-fxl) y2 dfxl) y3-ddf xl); while (abs(a)>1) x1 input("n Enter the value of initial guess again) yl-fxl) y2 di(xl) y3 ddfixl) a (yl y2(y2*y2) end x2-x1-(ylly2) while (abs(x2-x1)Pacc) x1-x2; yl=f(x1); end fprintfinn The root of equation is = %#x2); You can directly copy paste above program in matlab. Use values of initial guess as 5,7, and 10