Use Newton's method to approximate a root of the equation 3x' + 6x + 3 = 0 as follows. Let a1 = 2 be the initial approximation. The second approximation x2 is and the third approximation ¤3 is (Although these are approximations of the root, enter exact expressions for each approximation.)

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A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Let x⁷ + 4=0, x1=-1.  Use newton's method to find x3.

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Q: Find the root of the equation X2 - 4= In X , use X0=1.000, Solve by Simple Iterative method.

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Q: use Newton-Raphson method to obtain a root of equation x'-5x+3=0

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Q: Given a partially labeled graph as figure 2: (5,5) (13, 13) (8,2) (5,5) (8.7) (4.3) (6,6) (9,2)…

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Q: USE NEWTONS METHOD.  Find the 3rd estimate of the root of f(x)=x2-sin2x-1. . Use X0=0.5.

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Q: Use the identity 33 = 27 and linear approximation to estimate the value of (2.9). This estimate is…

A: Here we have to find the value of (2.9)³ using linear approximation. For that we use the identity…