Use the Bisection method to find solutions accurate to within 10-5 for the following problems. a....

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Use the Bisection method to find solutions accurate to within 10-5 for the following problems. a. x-2=0 for 0≤x≤1 he²-x²+3x-2=0 for 0 ≤x≤1 Question No. 2 Q/3. Determine the minimum number of iterations taken by the bisection method to solve x³+ 4.001x² + 4.002x + 1.101 = 0 in the interval [-0.5,0] within the accuracy of 0.5 x 10-² Question No. 3 Derive the recursive formula using Newton-Raphson method for finding the cube root and then evaluate √155. Question No. 4 Use Newton-Raphson method find a real root of the equation correct upto 4 d.p. xlog .ox = 4.77 Question No. 5 Derive the recursive formula using Newton-Raphson method for finding the reciprocal of a positive real number and then evaluate 1/5.. Question 6 Show that Newton-Raphson formula for finding pth root of a positive number N is given by (p-1)x, + N Use this formula to approximate the cube root of 25 within the accuracy of 10%. Question No. 7 Find a root of x-sin(x)=0 correct to four decimal places by Secant Method. Question No. 8 Use Secant method to compute the next two iterates. (i). Let f(x)=x²-2x-1, Start with p. = 2.6, and p =2.5. (ii). Let f(x)=x²-x-3, Start with p, 1.7, and p =1.67. Question No. 9 Show that the following equations have at least one solution in the given intervals. i. 2x cos(2x)-(x - 2)² = 0, x - (lnx)* = 0 [2,3] [4,5] ii. Page 1 of 2 Question No. 10 Use Secant method to find to find solution accurate to within 10 for the following problem. (i). 3xe¹=0 [1,2] (ii). 2x+3cosx-em0 [0.1] Use the Bisection method to find solutions accurate to within 10-5 for the following problems. a. x-2=0 for 0≤x≤1 he²-x²+3x-2=0 for 0 ≤x≤1 Question No. 2 Q/3. Determine the minimum number of iterations taken by the bisection method to solve x³+ 4.001x² + 4.002x + 1.101 = 0 in the interval [-0.5,0] within the accuracy of 0.5 x 10-² Question No. 3 Derive the recursive formula using Newton-Raphson method for finding the cube root and then evaluate √155. Question No. 4 Use Newton-Raphson method find a real root of the equation correct upto 4 d.p. xlog .ox = 4.77 Question No. 5 Derive the recursive formula using Newton-Raphson method for finding the reciprocal of a positive real number and then evaluate 1/5.. Question 6 Show that Newton-Raphson formula for finding pth root of a positive number N is given by (p-1)x, + N Use this formula to approximate the cube root of 25 within the accuracy of 10%. Question No. 7 Find a root of x-sin(x)=0 correct to four decimal places by Secant Method. Question No. 8 Use Secant method to compute the next two iterates. (i). Let f(x)=x²-2x-1, Start with p. = 2.6, and p =2.5. (ii). Let f(x)=x²-x-3, Start with p, 1.7, and p =1.67. Question No. 9 Show that the following equations have at least one solution in the given intervals. i. 2x cos(2x)-(x - 2)² = 0, x - (lnx)* = 0 [2,3] [4,5] ii. Page 1 of 2 Question No. 10 Use Secant method to find to find solution accurate to within 10 for the following problem. (i). 3xe¹=0 [1,2] (ii). 2x+3cosx-em0 [0.1]

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a To find the solution to the equation x 20 0 in the interval 0 1 using the bisection method we can follow these steps 1 Initialize the interval boundaries Set a 0 and b 1 2 Set the desired accuracy L... View the full answer