Answer to Question #342051 in Quantitative Methods for Belay

Question

1.Consider the equation xe^x = cos x

(a) Apply the intermediate value theorem to show that the function has a root in the interval

[0, 1].

(b) Find the real root using the secant method. Start with the two points, x1 = 0 and x2 = 1

and carry out the first four iterations.

(c) Find the real root using the Newton-Raphson method. Start with an initial approximation,

x0 = 0.5 correct to two decimal places.

2.Consider the initial value problem

dy = t(y + t) − 2, y(0) = 2. It is derivative of y respect to t

dt

(a) Use Eulers method with step sizes h = 0.3, h = 0.2 and h = 0.15, compute the approximations to y(0.6).

(b) Use the fourth order Runge-Kutta method Compute y(0.4) with h = 0.2.

Answer 1

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