2) Use Newtons method with the initial approximation x1 = -1 to find æ3, the third approxi- mation to the root of the equation x° + 2 = 0. Give your answer to four decimal places.

Q: Use Newton's method to approximate a root of the equation 2x + 3x2 + 2=0 as follows: Let 1 =-2 be…

A: Given:  f(x)=2x3+3x2+2=0and first approximation x1=-2Differentating f(x) with respect to "x"Then…

Q: Use Newton's method to approximate a nonzero solution of the equation 2sin(x)=x2sin(x)=x as follows.…

A: Let us assume a function f(x)=2sin(x)-xSo, f'(x)=2cos(x)-1

Q: 10 Show that the equation 2x+e" - 2 =0 has a root between x 0 and x= 1. Using the Newton- Raphson…

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Q: Use Newton's method to approximate a root of the equation 4x³ + 2x + 4 = 0 as follows. Let x₁ = 1 be…

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Q: Use Newton's method to approximate a root of the equation 3x^7+7x^4+2=0 as follows. Let x1=3  be the…

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Q: Use Newton's method to approximate a root of the equation 5x° + 7x + 1 = 0 as follows. Let x1 = 2 be…

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Q: Use Newton's method to approximate a root of the equation 5x' + 6x* + 4 = 0 as follows. Let æ1 = 3…

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Q: Which of these initial approximations does not work when using Newton's method to find the roots of…

A: For the Netwon method, f'(x) should be non zero.

Q: Use Newton's method to approximate a root of the equation 5x" + 7x + 2 = 0 as follows. Let x1 = 1 be…

A:

Q: Use Newton's method to approximate a root of the equation 3x' + 6x + 3 = 0 as follows. Let a1 = 2 be…

A: Consider the provided question, Given, 3x7+6x4+3=0Let  fx=3x7+6x4+3initial approximation x1=2 We…

Q: Use Newton's Method to find the two solutions of eª = 4xl to six significant figures. 12 1,0 -1…

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Q: 23.) Use Newton's Method to approximate V7 correct to six decimal places.

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Q: Use Newton's method to approximate a root of the equation 3x" + 4x* + 3 = 0 as follows. Let 21 = 1…

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Q: Use Newton's method with the specified initial approximation x1 to find x3, the third approximation…

A: We find the f'(x) using the power rule

Q: Use Newton's method to approximate a root of the equation cos (x² + 4) = x³ as follows. 2 be the…

A: Given equation is cosx2+4=x3. To approximate a root of the equation when x1=2.  Formula for Newton's…

Q: Use Newton's method to approximate a root of the equation 2a' + 7x + 2 = 0 as follows. Let z1 = 1 be…

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Q: Q1. What does the Newton's method produce to the actual root by repeating the approximation?

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Q: Apply the Newton-Raphson method to find the root of the equation: xsin x=4cosx, that is closer to 1.…

A: As per the requirement of the question we will apply the concept of Newton Raphson Method to reach…

Q: Use the Newton-Raphson method to find an approximate solution of the equatione-5x = xin the interval…

A: Let f(x) be defined as e-5x – x. In that case, we have to find the solution of the equation f(x) = 0…

Q: Starting with x = 4 apply just two steps of Newtons Method to estimate 2, show work

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Q: With an initial approximation of xo = 3, use Newton's Method to approximate /7, correct to at least…

A: Concept used: Newton’s Method If xn is an approximation of a solution of f(x)=0 and if f’(xn)≠0 then…

Q: 12) Use Newton's Method to find the closest root to xo =1 for f(x)=x-In(x+4)

A: Given: Function f(x)=x-ln(x+4) and x0=1To find: use newton method to find the root near to x0=1

Q: Take x = 2.5 as a first approximation to the root of the equation e* – 4x = 0 and apply Newton's…

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Q: Use Newton's method to approximate a root of the equation 4 sin(x) = x as follows. Let x1 = 1 be the…

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Q: Use Newton's method to approximate a root of the equation 5æ7 + 2x* + 3 = 0 as follows. Let z1 = 2…

A: Topic : Numerical method (Newton Raphson)

Q: 5. Use Newton's method to find the root, xx, of the equation, f(x) = x² e-- 0.6, up to machine…

A: Given: 5. f(x)=x2e-x-0.6 To find: Root of a given function using Newton's method starting with…

Q: To roughly estimate the locations of the roots of the equation +x + 3 = 0 and then approximate the…

A: The roots of the equation: f(x)=0 lies in the interval: a, b, if f(a)f(b)<0. Newtons method uses…

Q: Use Newton's method to approximate a root of the equation 2x^7+6x^4+2=0 as follows. Let x1=2  be the…

A: Given equation is : 2x7+6x4+2=0 Let fx=2x7+6x4+2 x1=2 To find second approximation and third…

Q: Use Newton's method to approximate a root of the equation 5x' + 4x* + 4 = 0 as follows. Let x1 = 2…

A: Given equation 5x7+4x4+4=0Let f(x)=5x7+4x4+4

Q: Use Newton's method to approximate a root of the equation cos (x² + 4) = 2³ as follows. Let x1 = 2…

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Q: 4. Find the smallest positive root of the equation a-r-10 = 0 using Newton Raphson method correct to…

A: Let fx=x4-x-10 ⇒f'x=4x3-1 Now f1=-10<0, f2=4>0 As f1f2<0 So,  by Intermediate value theorem…

Q: 1. Find the roots of the cubic equation x – 2x -5 = 0 correct to 2 decimal points using…

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Q: Write the formula for Newton's method and use the given initial approximation to compute the…

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Q: The first approximation P of the solution to the equation f(x) = 12 – 10 that is near to Po = 2…

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Q: Use Newton's method to approximate a root of the equation x° + x + 4 = 0 as follows. Let a1 = – 1 be…

A: Given: fx=x3+x+4 and x1=-1

Q: 3. Use Newton-Raphson method with x, =0.7 to find the root of the equation x-+2%3D0, where x>0. Give…

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Q: Use Newton's Method to make the second approximation x2 to the solution of 2e™ = ex. Take ₁ = 1.

A: To use Newton's method to make the second approximation to the solution of the below equation.…

Q: 3 Use Newton's method to approximate a root of the equation 5x + 7x + 2 = 0 as follows. Let 31 2 be…

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Q: Use Newton's method to approximate a root of the equation 3x' + 4x* + 3 = 0 as follows. Let æ1 = 2…

A: The Newton's method to approximate a root of the equation is:

Q: Use Newton's method with initial approximation x, = 1 to find x,, the second approximation to the…

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Q: Use Newton's method to approximate a root of the equation 2x + 5x* + 3 = 0 as follows. Let r1 = 1 be…

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Q: 6. Use Newton's method to find the third approximation to the root of: x* + 2x – 4 = 0. Use x,= 1 as…

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Q: For the equation sin⁡x=cos⁡(3x), use the Newton-Raphson method to find an approximate solution. Use…

A: *given:- sinx = cos3x. & x_0 = 0.5.

Q: Use Newton's method to approximate a root of the equation 4x' + 6x* + 3 = 0 as follows. Let x1 3 be…

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Q: Explain why Newtons method doesnt work for finding the root of the equation x³ – 3.x + 6 = 0 if the…

A: x3-3x+6=0 f(x)=x3-3x+6 f'(x)=ddxx3-3x+6=3x2-3 x0=1 --- Newton's method:- start with initial…

Q: Use Newton's method to approximate a root of the equation 21 + 3z+230 as follows: Let z1 =-2 be the…

A: Let's find.

Q: Write the formula for Newton's method and use the given initial approximation to compute the…

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Q: Use Newton's method to approximate a root of the equation 5 sin(x) = x as follows. Let x1 2 be the…

A: The given equation, 5 sin(x)=x

Q: Use Newton's method to approximate a root of the equation 2x+ 3z+2 0 as follows: Let z1 = -2 be the…

A: