Texts: 5. Use the Bisection method to find solutions accurate to within 10^(-5) for the following problems. a. x - 2^(-x) = 0 for 0 ≤ x ≤ 1 b. e^x - x^2 + 3x - 2 = 0 for 0 ≤ x ≤ 1 c. 2x cos(2x) - (x + 1)^2 = 0 for -3 ≤ x ≤ -2 and -1 ≤ x ≤ 0 d. x cos(x) - 2x^2 + 3x - 1 = 0 for 0.2 ≤ x ≤ 0.3 and 1.2 ≤ x ≤ 1.3 6. Use the Bisection method to find solutions, accurate to within 10^(-5) for the following problems. a. 3x - e^x = 0 for 1 ≤ x ≤ 2 b. 2x + 3 cos(x) - e^x = 0 for 0 ≤ x ≤ 1 c. x^2 - 4x + 4 - ln(x) = 0 for 1 ≤ x ≤ 2 and 2 ≤ x ≤ 4 d. x + 1 - 2 sin(πx) = 0 for 0 ≤ x ≤ 0.5 and 0.5 ≤ x ≤ 1
Added by Carrie M.
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We'll choose 5.a: \(x - 2^{-x} = 0\) for \(0 \leq x \leq 1\). ### Show more…
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SHOW YOUR COMPLETE SOLUTIONS" Solve the following: 1. Find a root of an equation f(x) = 2x^3 - 2x - 5 using the False Position method (regula falsi method) with 6 decimal places, given the initial interval is (a = 1, b = 2) at a required tolerance of f(x) < (-0.00011). 2. Find a root of an equation f(x) = x^3 - x - 1 using the Newton-Raphson method with 6 decimal places, given the initial x subscript 0 = 2 at a required tolerance of f(x) < 0.004. 3. Find a root of an equation f(x) = 2x^3 - 2x - 5 using the Secant method with 6 decimal places, given the initial interval is (a = 1, b = 2) at a required tolerance of f(x) < (-0.003). 4. Find a root of an equation f(x) = xlog10x - 1.2 using the Bisection method when the initial interval is (a = 2 and b = 3) such that the tolerance required is (b - a) < (0.00024) using 6 decimal places. 5. Find a root of an equation f(x) = 4.15x^3 - 2x + 5.15 using the Incremental Search method with a step-size requirement of 0.001 when the initial interval is (a = -2, b = -1) using 6 decimal places.
Sri K.
Use the Bisection method to find the solution accurate to within 10-5 for 2x cos (2x )-(x +1)2 = 0 on [-3,-2].
1. Use the bisection method with a hand calculator or computer to find the indicated roots of the following equations. Use an error tolerance of ̵ = 0.0001. (a) The real root of x³ - x² - x - 1 = 0. (b) The root of x = 1 + 0.3 cos(x). (c) The smallest positive root of cos(x) = 1/2 + sin(x). (d) The root of x = e⁻ˣ. (e) The smallest positive root of e⁻ˣ = sin(x). (f) The real root of x³ - 2x - 2 = 0. (g) All real roots of x⁴ - x - 1 = 0.
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