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- This is my lab assignment!!
This is my lab assignment!!
1. Determine the real root of f (x) = −26 + 85x − 91x^2 + 44x^3 − 8x^4 + x^5
:
(a) Using the bisection method to determine the root to εs = 10%.
(b) Using the false-position method and εs = 0.2 %.
Employ initial guesses of xl = 0.5 and xu = 1.0.
2. Given f (x) = −2x^6 − 1.6x^4 + 12x + 1
Use bisection to determine the maximum of this function. Employ initial guesses of
xl = 0 and xu = 1, and perform iterations until the approximate relative error falls
below 5%.
3. Determine the highest real root of f (x) = 0.95x^3 − 5.9x^2 + 10.9x − 6:
(a) Using the Newton-Raphson method (three iterations, xi = 3.5).
(b) Using the secant method (three iterations, xi–1 = 2.5 and xi = 3.5)
4. Determine the roots of the following simultaneous nonlinear equations using
(a) fixed-point iteration and
(b) the Newton-Raphson method:
y = −x^2 + x + 0.75
y + 5xy = x^2
Employ initial guesses of x = y = 1.2
:
(a) Using the bisection method to determine the root to εs = 10%.
(b) Using the false-position method and εs = 0.2 %.
Employ initial guesses of xl = 0.5 and xu = 1.0.
2. Given f (x) = −2x^6 − 1.6x^4 + 12x + 1
Use bisection to determine the maximum of this function. Employ initial guesses of
xl = 0 and xu = 1, and perform iterations until the approximate relative error falls
below 5%.
3. Determine the highest real root of f (x) = 0.95x^3 − 5.9x^2 + 10.9x − 6:
(a) Using the Newton-Raphson method (three iterations, xi = 3.5).
(b) Using the secant method (three iterations, xi–1 = 2.5 and xi = 3.5)
4. Determine the roots of the following simultaneous nonlinear equations using
(a) fixed-point iteration and
(b) the Newton-Raphson method:
y = −x^2 + x + 0.75
y + 5xy = x^2
Employ initial guesses of x = y = 1.2
Why don't you try some coding first? People here can help you to fix errors in your code, but we won't help you to work out your assignment.
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