PLEASE HELP QUESTION 3 Derive the Maclaurin series expansion for sin x. Then est

Question

PLEASE HELP QUESTION 3

Derive the Maclaurin series expansion for sin x. Then estimate the value of sin(pi/3) and include enough number of Maclaurin expansion terms so that the approximate error estimate falls below an error criterion conforming to three significant figures. Use zero- through third-order Taylor series expansions to predict f(2.5) for: f(x) = ln x using a base point at x = 1. Compute the true percent relative error epsilon_t for each approximation. Determine the maximum of following function by employing bisection method for [0, 1]. Calculate the approximate percent relative error and continue the iterations until this error is less than 5%: f(x) = -2x^6 - 1.5x^4 + 10x + 2 Use simple fixed-point iteration to find the roots of the following equation: f(x) = sin (Squareroot x) - x Use an initial guess of x_0 = 0.5 and iterate until epsilon_a

Explanation / Answer

F(x)=-2x^6-1.5x^4+10x+2 a b F(a) F(b) c=a+b/2 F(c) Update, If F(a)*F(c)

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