Computational Methods Exam Prep
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Find the root of the equation of $x^3 - 2x - 5 = 0$ using the secant method, correct to three decimal places.
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Apply the secant formula $x_{n+1} = x_n - f(x_n) \frac{x_n - x_{n-1}}{f(x_n) - f(x_{n-1})}$.
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Find the minimum value of $f(x) = x^2 + \frac{54}{x}$, within the interval $[0, 5]$ using the Fibonacci search method (n=3).
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Use Fibonacci search to minimize $f(x)$ by evaluating at points determined by Fibonacci ratios.
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Find the minimum value of $f(x) = 0.25x^4 - x^2 - 5x + 1$ in the interval $[0, 3]$ using Newton method given $\epsilon = 0.01$.
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Implement Newton's method iteratively until $|f'(x_n)| < \epsilon$.
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From the following table, estimate the number of students who obtained marks between 40 and 45:
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Use interpolation based on the frequency distribution provided.
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