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2 August, 10:59

Let f (x) = 2.912345x^2+3.131579x-0.099999

(a) to simplify approximation of f, write a quadratic function g (x) with integer coefficients that closely models f (x) for - 10 < x < 10.

(b) compute g (4) and f (4)

(c) compute the error in using g (4) to approximate f (4) as a percentage of the correct answer f (4)

(d) for larger values of x (say x = 10 or x = 20), would g (x) be an overestimate or an underestimate of f (x) ? justify your answer without computing specific values of f and g.

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  1. 2 August, 11:10
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    A.) Integers are positive and negative counting numbers. So, in order to find the integer coefficients, round off the coefficients in the equation to the nearest whole number. The function for g (x) is:

    g (x) = 3x²+3x

    B.) Substitute x=4 to the two functions.

    f (x) = 2.912345x² + 3.131579x-0.099999

    f (4) = 2.912345 (4) ²+3.131579 (4) - 0.099999

    f (4) = 59.023837

    g (x) = 3x²+3x

    g (4) = 3 (4) ²+3 (4)

    g (4) = 60

    C.) The percentage error is equal to:

    Percentage error = |g (4) - f (4) |/f (4) * 100

    Percentage error = |60 - 59.023837|/59.023837 * 100

    Percentage error = 1.65%

    D.) If x is a large number, for example x=10 or x=20, then g (x) would be an overestimate. This is because the value of x is raised to the power of 2. So, as the x increases, the corresponding function would increase exponentially. Even at x=4, g (x) is already an overestimate. What more for larger values of x? That means that the gap from the true answer f (x) would increase.
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