Question

Question 1 [15 marks] a) Derive the Newton’s iterative formula for finding the fourth root of positive number A, i.e. ?A. [5] b) Use the iterative formula obtained in (a) to compute ?270 correct to three decimal places. [4] c) Approximate using secant method the positive root of the function f(x) = x ? 0.2 sin x ? 0.5, Perform three iterations and truncate your answer to three significant digits. [6] Question 2 [15 marks] a) Consider the following function f(x) = e^2x cos 3x Let 0 ? x < 0.6 i) Construct a second-degree Lagrange interpolating polynomial for f(x), where the step size h = 0.3. Leave the polynomial in simplest form. [5] ii) Find the bound for absolute error on the interval [x0, xn]. [7] b) Find the percentage relative error in y at x = 1, if the error in x is 0.04, and y = 4x^6 ? 5x [3]

          Question 1 [15 marks]
a) Derive the Newton’s iterative formula for finding the fourth root of
positive number A, i.e. ?A. [5]
b) Use the iterative formula obtained in (a) to compute ?270 correct to
three decimal places. [4]
c) Approximate using secant method the positive root of the function
f(x) = x ? 0.2 sin x ? 0.5,
Perform three iterations and truncate your answer to three significant
digits. [6]
Question 2 [15 marks]
a)
Consider the following function
f(x) = e^2x cos 3x
Let 0 ? x < 0.6
i) Construct a second-degree Lagrange interpolating polynomial for f(x),
where the step size h = 0.3. Leave the polynomial in simplest form. [5]
ii) Find the bound for absolute error on the interval [x0, xn]. [7]
b)
Find the percentage relative error in y at x = 1, if the error in x is 0.04, and
y = 4x^6 ? 5x [3]

Question 1 [15 marks]
a) Derive the Newton’s iterative formula for finding the fourth root of
positive number A, i.e. ?A. [5]
b) Use the iterative formula obtained in (a) to compute ?270 correct to
three decimal places. [4]
c) Approximate using secant method the positive root of the function
f(x) = x ? 0.2 sin x ? 0.5,
Perform three iterations and truncate your answer to three significant
digits. [6]
Question 2 [15 marks]
a)
Consider the following function
f(x) = e^2x cos 3x
Let 0 ? x < 0.6
i) Construct a second-degree Lagrange interpolating polynomial for f(x),
where the step size h = 0.3. Leave the polynomial in simplest form. [5]
ii) Find the bound for absolute error on the interval [x0, xn]. [7]
b)
Find the percentage relative error in y at x = 1, if the error in x is 0.04, and
y = 4x^6 ? 5x [3]

Added by Samuel L.

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