Approximate ƒ(x) = x²/³ by a Taylor polynomial of degree 3 at a = 1 and find an upper bound for the error of your approximatio when 0.8 ≤ x ≤ 1.2.

1) Use Bisection to find a root of the function f(x) = ln x-2 on the interval [7, 8] to within 1 decimal place. Organize the results of all the calculations in the table below. You don't need to write down more than 5 decimal places. f(a.) C₁ ƒ (c₁) b₁ f(b) a₁ Half Interval Length

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Suppose that a continuous income stream has an annual rate of flow  f(t) = 500e−0.02t2  (in thousands of dollars per year). Use Simpson's Rule with  n = 4  to approximate the total income (in dollars) from this stream over the next 4 years. (Round your answer to the nearest dollar.)

Given f(x) = 1 divided by x+12, find the average rate of change of f (x) on the interval [8, 8 + h]. Your answer will be an expression involving h.

Consider the function E(x)=x2+6x-5. Compute the average rate of change of E(x) over the interval [a, a+ delta(x)], simplifying as much as possible. What happens to this expression for the average rate of change as x approaches zero?