NEED HELP ESPECIALLY ON C,D,E,F 2. [6pt] We attempt to find all solutions to f(x) = 0, where f(x) = e" – 3x – 1. (a) Sketch y = f(x) for -1 < x <3. How many solutions & does f(x) = 0 have? (b) Write code to implement the bisection method. Using the initial interval (1,3), write down the sequence of approximations X1, 22, 23, 24, 25 produced from your code. (c) What is the theoretical maximum value of...
You are given the values p0 = 0 , p1 = 1 and f(p1) = -1 . One interaction of the Secand method using p0 and p1 has been applied to f(x) to obtain p2 Aitken's delta^2 is the used. The result is p3 = 2/3. Determine f(p0)
' )y" + 6xy = 0 about x。:0. #2.) (15 points) For ( 1-X Find two linearly independent solutions y,(x) and V2(x) (that is solve the recurrence relation.) This problem is difficult, so plan your time accordingly ' )y" + 6xy = 0 about x。:0. #2.) (15 points) For ( 1-X Find two linearly independent solutions y,(x) and V2(x) (that is solve the recurrence relation.) This problem is difficult, so plan your time accordingly
(1) Use the Bisection method to find solutions accurate to within 10-2 for x3 – 7x2 + 14x – 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos X – X. (a). Approximate a root of f(x) using Fixed- point method accurate to within 10-2 . (b). Approximate a root of f(x) using Newton's method accurate to within 10-2. Find the second Taylor polynomial P2(x) for the function f(x) =...
Find two power series solutions of the given differential equation about the ordinary point x=0. (x^2+2)y"+6xy'-y=0 (Show all steps using y= please) nfiniti
Question 2 (20 Points) (1) Use the Bisection method to find solutions accurate to within 10-2 for x3 - 7x2 + 14x - 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos x - x. (a). Approximate a root of f(x) using Fixed-point method accurate to within 10-2 (b). Approximate a root of f(x) using Newton's method accurate to within 10-2.
(Variation of Parameters) (a) Find the two independent solutions x, (1) and x2 (t) of the homogeneous DE: x,-4x + 4x = 0 . (b) Find the Wronskian W(t) of your two solutions from Part (a). (c) Set up and solve the equations for the functions that we called c,() and c2(t), to use in finding a particular solution of the DE: x,,-4x + 4x = te2t Using Parts (a) and (c), set up the particular solution xp(t) Your answer...
using matlab 3. [1:2] Find a root (value of x for which f(x)-0) of f(x) = a x^3 + bx^2 + c x + d using Newton's interation: xnew = x -f(x)/(x). Note that f'(x) is the first derivative off with respect to x. Then x=xnew. Start with x=0 and iterate until f(xnew) < 1.0-4. Use values (a,b,c,d]=[-0.02, 0.09, -1.1, 3.2). Plot the polynomial vs x in the range (-10 10). Mark the zero point.
2. (a) We want to find the root x of the function f(x); that is, we need f(r) = 0 . This can be done using Newton's method, making use of the iterative formula f(xn) Show that the sequence ofiterates (%) converges quadratically if f'(x) 0 in some appropriate interval of x-values near the root χ 9 point b) We can get Newton's method to find the k-th root of some number a by making it solve the non-linear cquation...
Suppose f is continuous, f(0)=0, f(2)=2, f'(x)>0 and f (x) dx = 1. Find the value of the integral fro f-?(x) dx =?