14) Bisection Method for Approximating Zeros of a Function f We begin with two consecutive integers, a and a + 1, such that f(a) and f(a + 1) are of opposite sign. Evaluate f at the midpoint m, of a and a + 1. If f(m,) = 0, then mị is the zero of f, and we are finished. Otherwise, f (m,) is of opposite sign to either f(a) or f(a + 1). Suppose that it is f (a) and f(m1) that are of opposite sign. Now evaluate f at the midpoint m2 of a and m1. Repeat this process until the desired degree of accuracy is obtained. Note that each of these iterations places the zero in an interval whose length is half that of the previous interval. Use the bisection method to approximate the zero of f (x) = 8x* – 2x² + 5x – 1 in the interval [0,1] correct to three decimal places. Hint: The process ends when both endpoints agree to the desired number of decimal places.

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A: a) finding the inverse of f(x)

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A:

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A:

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A:

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A:

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A: Given function is f:ℝ→ℝ such that fx = 2x3 - 7

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A: We need to proveor disprove if  fa+fb=fa+b

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A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.