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- Use the bisection method to find the approximation to the root of the equation f(x) = x3 - 2x - 1 that is located interval [0, 2].Use a second Taylor polynomial at x = 0 to estimate the areaunder the curve y = ln(1 + x^2) from x = 0 to x = 1/2Find the minimum value of n that guarantees an error of no more than 1/30,000 in approximating the integral 1/x dx [3,4] by the Trapezoidal Rule with n equal subintervals.
- In the given question as folows use Taylor’s Theorem to obtain an upper bound for the error of the approximation. Then calculate the exact value of the error :-Find a root of a equation f(x) = 2x³ - 2x - 5 Using secant bisection method when the initial interval is (a= 1, b= 2) at a required tolerance of f(x)←(-0.003).The Bisection Method is used to approximate the root of the eqaution f(x) =x³+ 1.2x² – 4x – 4.8 = 0 on [-1.5, – 1]. Then the second approximation(p2) of the root is
- Find the area bounded by the following: 1. Curve y²-8y-8x +32= 0 and y²-8y + 4x = 0calculate y(0,1) with the interval Δx = 0.025 using the Runge Kutta order 3 and Runge-kutta order 4 methodsa. Use the Trapezoidal Rule with n = 10 to approximate the integral b. Give an upper bound for the error involved in the approximation.