1. Locate a root of sin(x)=x2 where x is in radians. Use a graphical technique and...

1. Locate a root of sin(x)=x2 where x is in radians. Use a graphical technique and bisection with
the initial interval from 0.5 to 1. Perform the computation until ea is less than es=2%. Also
perform an error check by substituting your final answer into the original equation.
2. Determine the positive real root of ln(x
2
)=0.7 using three iterations of the bisection method,
with initial interval of [0.5:2].
3. Determine the lowest positive root of f(x)=7sin(x)e
-x
-1 using (a) the Newton-Raphson
method (three iterations, xi=0.3). (b) the secant method (five iterations, xi-1=0.5 and xi=0.4). (c)
the modified secant method (three iterations, xi=0.3, δ=0.01).
4. Use the Newton-Raphson method to find the root of f(x)=e
-0.5x
(4-x)-2. Employ initial guesses
of (a) 2, (b) 6, and (c) 8. Explain your results.

Expert Solution

Colby Messinger answered 1 year ago

sin(tan-1 x), where |x| < 1, is equal to: (a) x/√(1 – x2) (b) 1/√(1 – x2) (c) 1/√(1 + x2) (d) x/√(1 + x2)

sin(tan-1 x), where |x| < 1, is equal to:(a) x/√(1 – x²)(b) 1/√(1 – x²)(c) 1/√(1 + x²)(d) x/√(1 + x²)

use bisection to find the real root x = sin(x) + 1 with the initial guesses...

use bisection to find the real root x = sin(x) + 1 with the initial guesses of x l = 0 and x u = 3. perform the computation until the approximate error falls below 5%

Find the root of the function f(x) = 8 - 4.5 ( x - sin x...

Find the root of the function f(x) = 8 - 4.5 ( x - sin x ) in the interval [2,3]. Exhibit a numerical solution using Newton method.

Use the False Position method to find a guess of the root of f(x) = cos(x2...

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The number of points in (-∞, ∞) for which x2 – x sin x – cos x = 0 is

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Use false position method to find the root of ?(?) = −sin(? − 5) + ?...

Use false position method to find the root of ?(?) = −sin(? − 5) + ? with initial guesses of 0.2 and 1. Show up to three iterations and calculate the relative percent error ?? for each iteration possible? Show full details for at least one iteration to get full points. Also, if three significant figure accuracy is required, show if the value after third iteration is acceptable or not.

The function Sine is defined as: where x is an angle in radians Write a Matlab...

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Given that h(x) = x.sinx . Find the root of the function h(x) = 1, where...

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Let f(x) = sin(πx). • x0 = 1,x1 = 1.25, and x2 = 1.6 are given....

Let f(x) = sin(πx). • x0 = 1,x1 = 1.25, and x2 = 1.6 are given. Construct Newton’s DividedDiﬀerence polynomial of degree at most two. • x0 = 1,x1 = 1.25,x2 = 1.6 and x3 = 2 are given. Construct Newton’s Divided-Diﬀerence polynomial of degree at most three.

Using Matlab 1. Solve the following equations set f1 (x1,x2) = sin (sin (x1)) +x2 f2...

Using Matlab 1. Solve the following equations set f1 (x1,x2) = sin (sin (x1)) +x2 f2 (x1,x2) = x1+ e^(x2) a) Can this equation set be solved by the fixed - point method with the following expressions? And why? Show your analysis with a 2D graph. g1 (x1,x2) = -e^(x2) g2 (x1,x2) = -sin⁡(x1) b) Use Newton Raphson Method with initial values x1 = -2, x2 = 1.5. (8 significant figures. Please submit the code and results.)

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