Use the Bisection method to find solutions to within 10-6 a. x³ + 3x² − 1 = 0, [−3,−2] - b. ex - 3x² = 0, [0,1] Components Complete Table of iteration and approximation Near Tolerance Near magnitude of the result Total
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- a- Show that the equation x^3 + 9x − 4 = 0 has exactly one solution p^∗in the interval [0, 1]. b- Use the Bisection method to find the first two approximations (p1 andp2) for p^*.Determine the real root of 5x^3 − 5x^2 + 6x − 2 using bisection method to locate the root. Employ initial guess of xl = 0 xu = 1 until the approximate error falls below εs = 0.2%.Use the Bisection Method to locate a solution of x 2 - 7 = 0 to two decimal places
- Prior to entering in the corresponding input fields, all numerical answers should be rounded to 6-digit floating-point numbers. Given a real number z, the symbol z˜ denotes the result of rounding of z to a 6-digit floating-point number. i)use the Bisection method to find an approximation pN of the unique solution p the equation 3.60x(1-x2+x)In(x)=x2-1 in[a,b]=[0.05,0.5] such that RE(p˜N≈p˜N-1)<10-3.The equation f (x) = 2 − x2 sin x = 0 has a solution in the interval [-1,2]. Compute p3 for the Bisection method.E. Use the method of bisection to approximate √5 to within 0.01. Begin by noticing that x2 - 5 has a zero between 2 and 3.
- Use the secant method to find solutions to within 10^-4 for x^3 - 2x^2 - 5=0, [1,4]consider y'=-2y,y(0)=1 and analytic solution is y(x)=e^-2x a.Approximate y(0.1) using two steps of Euler's method b. Verify that the global truncation error for Euler's methos is O(h) by comparing the errors in parts (a) and (d).Let p be the unique root of x^5 + 4x − 11 = 0 in the interval [a1, b1] = [1, 2],and pn be the midpoint of the interval [an, bn] used for the nth bisection. How large should n be to ensure that |pn − p| < 10^−14 according to the error estimate for the Bisection Method?
- Use Euler method to approximate the value of y(0.2), given ay' - by = kcos(cx) + mx , y(0) = 5 with Δx = 0.025 if a = 2, b = 4, k = 6, c = 2, and m = 7 Round off the final answer to five decimal places but do not round off on previous calculations.Calculate 3 iterations of the Bisection Method to find the Zero of the function "e^x-2" in I = [0, 1]. How many iterarions would be necessary to find an aproach of this Zero with precision ∈ = 10^-513??Carry out the five iterations of by using bisection method. F(x)=xcosx-2x^2+3x-1 0<=x<=1